What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

AP Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card AP Physics 1 review of concepts, formulas, graphs, experiments, and reasoning across all eight course units.

Avtor Open Study Contributor

O tem kompletu

This 400-card deck reviews all eight AP Physics 1 course units: Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs.

The deck does not mechanically reverse every fact. Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded.

The sequence follows Units 1–8 so motion, forces, energy, and momentum become prerequisites for rotation, orbits, oscillations, and fluids. Definitions appear before dependent uses, while related formula, graph, condition, calculation, and contrast prompts are separated where practical to reduce short-range cueing.

Course scope was checked against the official AP Physics 1 course page. Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of physics facts or third-party material.

This is an independently authored, unofficial educational deck. It is not affiliated with, sponsored by, or endorsed by the College Board. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product. No AP exam questions, answer keys, scoring guidelines, curriculum text, logos, or trade dress were copied.

Kartice v tem kompletu

Kartica 1
Vprašanje
What separates a vector quantity from a scalar quantity?
Odgovor
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Kartica 2
Vprašanje
When is the point-object model useful in kinematics?
Odgovor
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Kartica 3
Vprašanje
When may the constant-acceleration kinematic equations be used?
Odgovor
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Kartica 4
Vprašanje
Why must a velocity statement name or imply a reference frame?
Odgovor
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Kartica 5
Vprašanje
Why can horizontal and vertical projectile motion be analyzed separately?
Odgovor
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Kartica 6
Vprašanje
Can an object have zero velocity and nonzero acceleration at one instant?
Odgovor
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Kartica 7
Vprašanje
A runner completes one lap and returns to the start. How do distance and displacement compare?
Odgovor
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Kartica 8
Vprašanje
What makes a reference frame convenient for a motion problem?
Odgovor
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Kartica 9
Vprašanje
How are the components of a launch velocity v at angle θ found?
Odgovor
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Kartica 10
Vprašanje
What does average velocity measure?
Odgovor
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Kartica 11
Vprašanje
Do a vector's magnitude and its component use different SI units?
Odgovor
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Kartica 12
Vprašanje
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Odgovor
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Kartica 13
Vprašanje
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Odgovor
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Kartica 14
Vprašanje
What does average acceleration measure?
Odgovor
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Kartica 15
Vprašanje
What does a negative one-dimensional vector component mean?
Odgovor
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Kartica 16
Vprašanje
For constant acceleration, what does v = v₀ + at retrieve?
Odgovor
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Kartica 17
Vprašanje
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Odgovor
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Kartica 18
Vprašanje
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Odgovor
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Kartica 19
Vprašanje
What does the slope of a position-versus-time graph represent?
Odgovor
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Kartica 20
Vprašanje
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Odgovor
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Kartica 21
Vprašanje
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Odgovor
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Kartica 22
Vprašanje
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Odgovor
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Kartica 23
Vprašanje
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Odgovor
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Kartica 24
Vprašanje
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Odgovor
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Kartica 25
Vprašanje
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Odgovor
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Kartica 26
Vprašanje
Why can average speed differ from the magnitude of average velocity?
Odgovor
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Kartica 27
Vprašanje
What does the slope of a velocity-versus-time graph represent?
Odgovor
Acceleration. The slope's units are (m/s)/s = m/s².
Kartica 28
Vprašanje
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Odgovor
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Kartica 29
Vprašanje
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Odgovor
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Kartica 30
Vprašanje
Can an object have nonzero velocity and zero acceleration?
Odgovor
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Kartica 31
Vprašanje
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Odgovor
Position x versus t². Its slope is ½a when the initial velocity is zero.
Kartica 32
Vprašanje
What does signed area under a velocity-versus-time graph represent?
Odgovor
Displacement. Area below the time axis contributes negative displacement.
Kartica 33
Vprašanje
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Odgovor
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Kartica 34
Vprašanje
How can a motion sensor test whether a cart moves at constant velocity?
Odgovor
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Kartica 35
Vprašanje
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Odgovor
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Kartica 36
Vprašanje
Which constant-acceleration equation connects speed and displacement without using time?
Odgovor
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Kartica 37
Vprašanje
How could video data test the independence of projectile components?
Odgovor
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Kartica 38
Vprašanje
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Odgovor
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Kartica 39
Vprašanje
How can average velocity over a very short interval approximate instantaneous velocity?
Odgovor
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Kartica 40
Vprašanje
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Odgovor
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Kartica 41
Vprašanje
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Odgovor
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Kartica 42
Vprašanje
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Odgovor
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Kartica 43
Vprašanje
What does signed area under an acceleration-versus-time graph represent?
Odgovor
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Kartica 44
Vprašanje
How is one-dimensional relative velocity calculated for two objects A and B?
Odgovor
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Kartica 45
Vprašanje
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Odgovor
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Kartica 46
Vprašanje
What does choosing a system boundary decide in a mechanics problem?
Odgovor
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Kartica 47
Vprašanje
What belongs on a free-body diagram for one chosen object?
Odgovor
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Kartica 48
Vprašanje
What assumptions define the ideal-string model used in introductory algebra-based physics?
Odgovor
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Kartica 49
Vprašanje
What does translational equilibrium require?
Odgovor
Zero net force. The object may be at rest or move with constant velocity.
Kartica 50
Vprašanje
In an inertial frame, how does Newton's second law connect force and motion?
Odgovor
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Kartica 51
Vprašanje
How do mass and weight differ?
Odgovor
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Kartica 52
Vprašanje
How does static friction choose its magnitude before slipping begins?
Odgovor
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Kartica 53
Vprašanje
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Odgovor
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Kartica 54
Vprašanje
What direction does centripetal acceleration point in circular motion?
Odgovor
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Kartica 55
Vprašanje
What is the gravitational force magnitude between two point masses?
Odgovor
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Kartica 56
Vprašanje
Why isn't the normal force always equal to an object's weight?
Odgovor
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Kartica 57
Vprašanje
What determines a friction coefficient in the simple model?
Odgovor
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Kartica 58
Vprašanje
What is the centripetal-acceleration magnitude for speed v and radius r?
Odgovor
a_c = v²/r. It is a kinematic requirement, not a separate force.
Kartica 59
Vprašanje
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Odgovor
It is greater than the weight. Upward net force requires N - mg > 0.
Kartica 60
Vprašanje
What does a spring constant k measure, and what is its SI unit?
Odgovor
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Kartica 61
Vprašanje
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Odgovor
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Kartica 62
Vprašanje
What provides centripetal force?
Odgovor
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Kartica 63
Vprašanje
How is near-surface gravitational field strength related to weight?
Odgovor
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Kartica 64
Vprašanje
How is weight resolved on an incline of angle θ measured from horizontal?
Odgovor
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Kartica 65
Vprašanje
What does Newton's third law say about an interaction between objects A and B?
Odgovor
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Kartica 66
Vprašanje
What does signed tangential acceleration describe during circular motion?
Odgovor
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Kartica 67
Vprašanje
What happens to gravitational force if the separation between two point masses doubles?
Odgovor
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Kartica 68
Vprašanje
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Odgovor
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Kartica 69
Vprašanje
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Odgovor
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Kartica 70
Vprašanje
Which tension components act for a conical pendulum?
Odgovor
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Kartica 71
Vprašanje
What does apparent weight measure for an object supported by one surface?
Odgovor
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Kartica 72
Vprašanje
How are several forces combined to find net force?
Odgovor
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Kartica 73
Vprašanje
Why is tension uniform along one continuous ideal string?
Odgovor
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Kartica 74
Vprašanje
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Odgovor
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Kartica 75
Vprašanje
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Odgovor
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Kartica 76
Vprašanje
For the same net force, what happens to acceleration if mass doubles?
Odgovor
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Kartica 77
Vprašanje
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Odgovor
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Kartica 78
Vprašanje
How are radial and tangential acceleration combined when circular speed changes?
Odgovor
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Kartica 79
Vprašanje
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Odgovor
It is twice as large. Surface field strength follows g = GM/R².
Kartica 80
Vprašanje
Does a force have to point in the direction of motion?
Odgovor
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Kartica 81
Vprašanje
Where is the center of mass of a uniform object with a symmetric mass distribution?
Odgovor
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Kartica 82
Vprašanje
How are speed, period, and frequency related in uniform circular motion?
Odgovor
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Kartica 83
Vprašanje
Why is an object apparently weightless in free fall?
Odgovor
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Kartica 84
Vprašanje
Can forces balance along one axis while an object accelerates along another?
Odgovor
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Kartica 85
Vprašanje
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Odgovor
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Kartica 86
Vprašanje
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Odgovor
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Kartica 87
Vprašanje
What motion results when the net force on an object is zero in an inertial frame?
Odgovor
Constant velocity. Rest is the special case with constant velocity equal to zero.
Kartica 88
Vprašanje
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Odgovor
4 m/s². Use a = ΣF/m = 12/3.
Kartica 89
Vprašanje
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Odgovor
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Kartica 90
Vprašanje
Does friction in the simple dry-friction model depend on apparent contact area?
Odgovor
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Kartica 91
Vprašanje
When should Hooke's-law predictions be treated cautiously?
Odgovor
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Kartica 92
Vprašanje
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Odgovor
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Kartica 93
Vprašanje
Why do internal forces cancel when finding the net force on a complete system?
Odgovor
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Kartica 94
Vprašanje
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Odgovor
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Kartica 95
Vprašanje
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Odgovor
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Kartica 96
Vprašanje
What does inertia describe?
Odgovor
An object's resistance to changes in velocity. Mass measures translational inertia.
Kartica 97
Vprašanje
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Odgovor
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Kartica 98
Vprašanje
Does zero net force mean no forces act?
Odgovor
No. Several forces can act and cancel vectorially.
Kartica 99
Vprašanje
What is the common model for kinetic-friction magnitude?
Odgovor
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Kartica 100
Vprašanje
How could hanging masses measure the spring constant of one ideal spring?
Odgovor
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Kartica 101
Vprašanje
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Odgovor
It becomes four times as large. F_in = mv²/r depends on speed squared.
Kartica 102
Vprašanje
Where is the center of mass of two point masses on an x-axis?
Odgovor
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Kartica 103
Vprašanje
Why must net force, rather than one selected force, be used in ΣF = ma?
Odgovor
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Kartica 104
Vprašanje
Why can tension vary along a hanging chain with nonnegligible mass?
Odgovor
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Kartica 105
Vprašanje
What makes a reference frame inertial?
Odgovor
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Kartica 106
Vprašanje
How could carts test the proportionality between acceleration and net force?
Odgovor
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Kartica 107
Vprašanje
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Odgovor
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Kartica 108
Vprašanje
Which direction does kinetic friction act?
Odgovor
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Kartica 109
Vprašanje
What does the slope of a spring-force-versus-displacement graph give?
Odgovor
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Kartica 110
Vprašanje
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Odgovor
v_min = √(gr). At the threshold, the support force or tension is zero.
Kartica 111
Vprašanje
What is translational kinetic energy?
Odgovor
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Kartica 112
Vprašanje
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Odgovor
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Kartica 113
Vprašanje
What does power measure?
Odgovor
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Kartica 114
Vprašanje
What does conservation of energy say for an isolated system?
Odgovor
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Kartica 115
Vprašanje
Can translational kinetic energy be negative?
Odgovor
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Kartica 116
Vprašanje
What does negative work by a force mean?
Odgovor
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Kartica 117
Vprašanje
What is the near-surface change in gravitational potential energy?
Odgovor
ΔU_g = mgΔy. It applies when g can be treated as constant.
Kartica 118
Vprašanje
When is a chosen system's mechanical energy K + U conserved?
Odgovor
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Kartica 119
Vprašanje
What is the SI unit of power?
Odgovor
The watt, W. One watt equals one joule per second.
Kartica 120
Vprašanje
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Odgovor
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Kartica 121
Vprašanje
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Odgovor
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Kartica 122
Vprašanje
Does choosing a different zero level for potential energy change physical predictions?
Odgovor
No. Only potential-energy differences enter measurable energy changes.
Kartica 123
Vprašanje
Can an engine do the same work with different average power?
Odgovor
Yes. Doing the same work in less time requires greater average power.
Kartica 124
Vprašanje
When does a constant nonzero force do zero work over an interval?
Odgovor
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Kartica 125
Vprašanje
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Odgovor
No. With only gravity doing work, the potential-energy change depends on height, not path.
Kartica 126
Vprašanje
How does translational kinetic energy change if speed doubles at constant mass?
Odgovor
It becomes four times as large. Kinetic energy depends on v².
Kartica 127
Vprašanje
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Odgovor
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Kartica 128
Vprašanje
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Odgovor
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Kartica 129
Vprašanje
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Odgovor
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Kartica 130
Vprašanje
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Odgovor
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Kartica 131
Vprašanje
A machine transfers 600 J in 3 s. What is its average power?
Odgovor
200 W. Divide energy transferred by elapsed time.
Kartica 132
Vprašanje
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Odgovor
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Kartica 133
Vprašanje
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Odgovor
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Kartica 134
Vprašanje
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Odgovor
They are equal. Kinetic energy uses speed and has no direction.
Kartica 135
Vprašanje
What makes work by a conservative force path independent?
Odgovor
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Kartica 136
Vprašanje
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Odgovor
30 J. Here θ = 0, so W = Fd = 10×3.
Kartica 137
Vprašanje
How is total potential energy built for a system with several interacting pairs?
Odgovor
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Kartica 138
Vprašanje
How should external work appear in an energy equation?
Odgovor
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Kartica 139
Vprašanje
How does a spring launch problem combine energy forms?
Odgovor
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Kartica 140
Vprašanje
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Odgovor
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Kartica 141
Vprašanje
How does translational kinetic energy change if mass triples at constant speed?
Odgovor
It triples. Kinetic energy is directly proportional to mass.
Kartica 142
Vprašanje
How much net work does a conservative force do around a path that returns to the initial configuration?
Odgovor
Zero. The initial and final potential energies are the same.
Kartica 143
Vprašanje
Where is stable equilibrium on a potential-energy-versus-position graph?
Odgovor
At a local minimum. Small displacements produce forces that point back toward the minimum.
Kartica 144
Vprašanje
Which displacement belongs in the work done by a force on a rigid object?
Odgovor
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Kartica 145
Vprašanje
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Odgovor
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Kartica 146
Vprašanje
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Odgovor
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Kartica 147
Vprašanje
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Odgovor
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Kartica 148
Vprašanje
How can force-sensor data measure work when force changes as its point of application moves?
Odgovor
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Kartica 149
Vprašanje
Why is potential energy assigned to a system rather than one isolated object?
Odgovor
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Kartica 150
Vprašanje
How can work by a nonconservative force depend on path?
Odgovor
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Kartica 151
Vprašanje
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Odgovor
9 J. K = ½(2)(3²) = 9 J.
Kartica 152
Vprašanje
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Odgovor
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Kartica 153
Vprašanje
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Odgovor
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Kartica 154
Vprašanje
Why are energy bar charts useful?
Odgovor
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Kartica 155
Vprašanje
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Odgovor
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Kartica 156
Vprašanje
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Odgovor
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Kartica 157
Vprašanje
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Odgovor
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Kartica 158
Vprašanje
What does a steep potential-energy graph imply about force magnitude in one dimension?
Odgovor
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Kartica 159
Vprašanje
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Odgovor
10 J. U_s = ½(80)(0.50²).
Kartica 160
Vprašanje
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Odgovor
200 W. P = Fv_point = 50 × 4.
Kartica 161
Vprašanje
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Odgovor
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Kartica 162
Vprašanje
Does an object's translational kinetic energy depend on the reference frame?
Odgovor
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Kartica 163
Vprašanje
Why can work depend on the system boundary?
Odgovor
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Kartica 164
Vprašanje
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Odgovor
12 J. The signed area is ½×4×6.
Kartica 165
Vprašanje
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Odgovor
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Kartica 166
Vprašanje
What is the clearest first step in an energy-conservation problem?
Odgovor
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Kartica 167
Vprašanje
Why can energy methods solve some problems without finding time?
Odgovor
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Kartica 168
Vprašanje
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Odgovor
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Kartica 169
Vprašanje
What is the SI unit of kinetic energy?
Odgovor
The joule, J. One joule equals 1 kg·m²/s².
Kartica 170
Vprašanje
How is work by a conservative force related to potential-energy change?
Odgovor
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Kartica 171
Vprašanje
Where is unstable equilibrium on a potential-energy-versus-position graph?
Odgovor
At a local maximum. A small displacement produces a force that pushes the system farther away.
Kartica 172
Vprašanje
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Odgovor
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Kartica 173
Vprašanje
Why should thermal energy not be written as a force?
Odgovor
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Kartica 174
Vprašanje
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Odgovor
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Kartica 175
Vprašanje
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Odgovor
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Kartica 176
Vprašanje
What is linear momentum?
Odgovor
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Kartica 177
Vprašanje
How is a multi-object system's total momentum found?
Odgovor
Add every object's momentum as a vector. In one dimension, add signed values.
Kartica 178
Vprašanje
For a chosen object or system, what is external impulse?
Odgovor
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Kartica 179
Vprašanje
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Odgovor
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Kartica 180
Vprašanje
Why can two objects bounce apart yet still collide inelastically?
Odgovor
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Kartica 181
Vprašanje
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Odgovor
+12 kg·m/s. p = mv = 3 × 4.
Kartica 182
Vprašanje
Why can momentum be negative while kinetic energy cannot?
Odgovor
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Kartica 183
Vprašanje
When is a system's total linear momentum conserved?
Odgovor
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Kartica 184
Vprašanje
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Odgovor
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Kartica 185
Vprašanje
Can total kinetic energy increase in an explosion?
Odgovor
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Kartica 186
Vprašanje
How is total momentum related to center-of-mass velocity?
Odgovor
p_total = Mv_cm. M is the system's total mass.
Kartica 187
Vprašanje
How does a nonzero external impulse affect system momentum?
Odgovor
It changes total momentum by that impulse. J_external = Δp_system.
Kartica 188
Vprašanje
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Odgovor
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Kartica 189
Vprašanje
What are equivalent SI units for impulse?
Odgovor
N·s and kg·m/s. Both represent a change in momentum.
Kartica 190
Vprašanje
What defines an elastic collision?
Odgovor
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Kartica 191
Vprašanje
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Odgovor
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Kartica 192
Vprašanje
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Odgovor
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Kartica 193
Vprašanje
Why must momentum signs be kept through an impulse calculation?
Odgovor
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Kartica 194
Vprašanje
What defines a perfectly inelastic collision?
Odgovor
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Kartica 195
Vprašanje
Why can momentum be conserved during a collision even when large forces act?
Odgovor
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Kartica 196
Vprašanje
Two objects have equal speed. Which has the larger momentum magnitude?
Odgovor
The object with larger mass. At equal speed, momentum is proportional to mass.
Kartica 197
Vprašanje
How is momentum conservation written for a two-dimensional isolated interaction?
Odgovor
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Kartica 198
Vprašanje
For a chosen object or system, how is average net external force related to impulse?
Odgovor
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Kartica 199
Vprašanje
Which conservation law alone can determine the shared final velocity of a sticking collision?
Odgovor
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Kartica 200
Vprašanje
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Odgovor
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
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Kartica 201
Vprašanje
If external impulse during a collision is small but not zero, what should experimental data show?
Odgovor
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Kartica 202
Vprašanje
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Odgovor
It does not change. Impulse depends on total signed area, not peak force alone.
Kartica 203
Vprašanje
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Odgovor
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Kartica 204
Vprašanje
How can a nearly frictionless cart track improve a momentum-conservation test?
Odgovor
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Kartica 205
Vprašanje
How does an object's momentum change if its speed doubles at constant mass?
Odgovor
Its momentum magnitude doubles. Momentum depends linearly on speed.
Kartica 206
Vprašanje
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Odgovor
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Kartica 207
Vprašanje
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Odgovor
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Kartica 208
Vprašanje
Why is sticking evidence of an inelastic collision?
Odgovor
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Kartica 209
Vprašanje
Can a moving two-object system have zero total momentum?
Odgovor
Yes. Equal and opposite momenta cancel even though each object is moving.
Kartica 210
Vprašanje
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Odgovor
3 N·s in the force direction. Multiply the net external force by the interaction time.
Kartica 211
Vprašanje
What does a momentum-versus-velocity graph's slope represent for one object?
Odgovor
Its mass. The relationship p = mv is linear through the origin.
Kartica 212
Vprašanje
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Odgovor
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Kartica 213
Vprašanje
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Odgovor
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Kartica 214
Vprašanje
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Odgovor
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Kartica 215
Vprašanje
What remains conserved in an isolated inelastic collision?
Odgovor
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Kartica 216
Vprašanje
Why does choosing both colliding objects as the system simplify momentum analysis?
Odgovor
Their contact forces become internal. Only external impulse can change the system total.
Kartica 217
Vprašanje
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Odgovor
Net external force. A steeper slope means a larger force in the slope's signed direction.
Kartica 218
Vprašanje
Why do airbags reduce injury force during a stop?
Odgovor
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Kartica 219
Vprašanje
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Odgovor
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Kartica 220
Vprašanje
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Odgovor
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Kartica 221
Vprašanje
What is angular displacement?
Odgovor
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Kartica 222
Vprašanje
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Odgovor
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Kartica 223
Vprašanje
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Odgovor
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Kartica 224
Vprašanje
What does rotational inertia measure?
Odgovor
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Kartica 225
Vprašanje
What is the lever arm in a torque calculation?
Odgovor
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Kartica 226
Vprašanje
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Odgovor
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Kartica 227
Vprašanje
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Odgovor
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Kartica 228
Vprašanje
How is rotational inertia found for a collection of point masses?
Odgovor
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Kartica 229
Vprašanje
What determines the magnitude of torque from one force about a chosen axis?
Odgovor
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Kartica 230
Vprašanje
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Odgovor
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Kartica 231
Vprašanje
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Odgovor
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Kartica 232
Vprašanje
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Odgovor
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Kartica 233
Vprašanje
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Odgovor
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Kartica 234
Vprašanje
How are clockwise and counterclockwise torques combined?
Odgovor
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Kartica 235
Vprašanje
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Odgovor
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Kartica 236
Vprašanje
Why must an axis be named when stating rotational inertia?
Odgovor
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Kartica 237
Vprašanje
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Odgovor
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Kartica 238
Vprašanje
Why is torque's unit N·m not called a joule?
Odgovor
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Kartica 239
Vprašanje
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Odgovor
4 rad/s². |α| = |Στ_external|/I = 8/2.
Kartica 240
Vprašanje
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Odgovor
At the object's center of mass. That single force gives the same net gravitational force and torque.
Kartica 241
Vprašanje
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Odgovor
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Kartica 242
Vprašanje
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Odgovor
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Kartica 243
Vprašanje
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Odgovor
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Kartica 244
Vprašanje
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Odgovor
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Kartica 245
Vprašanje
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Odgovor
The hoop. More of its mass lies far from the axis.
Kartica 246
Vprašanje
Why can a rigid object have zero net external force but nonzero net external torque?
Odgovor
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Kartica 247
Vprašanje
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Odgovor
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Kartica 248
Vprašanje
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Odgovor
4 N·m. τ = rF for a perpendicular force.
Kartica 249
Vprašanje
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Odgovor
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Kartica 250
Vprašanje
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Odgovor
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Kartica 251
Vprašanje
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Odgovor
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Kartica 252
Vprašanje
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Odgovor
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Kartica 253
Vprašanje
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Odgovor
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Kartica 254
Vprašanje
Does moving the chosen pivot change an individual force's torque?
Odgovor
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Kartica 255
Vprašanje
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Odgovor
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Kartica 256
Vprašanje
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Odgovor
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Kartica 257
Vprašanje
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Odgovor
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Kartica 258
Vprašanje
How could a meterstick experiment test torque balance?
Odgovor
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Kartica 259
Vprašanje
For uniform rotation at frequency f, what is the angular-speed magnitude?
Odgovor
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Kartica 260
Vprašanje
Why is choosing the pivot at an unknown support force often useful?
Odgovor
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Kartica 261
Vprašanje
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Odgovor
The parallel axis through the center of mass. Any offset adds the positive term Md².
Kartica 262
Vprašanje
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Odgovor
It becomes one-third as large. For each stated system, α = Στ_external/I.
Kartica 263
Vprašanje
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Odgovor
3 m/s. v_t = r|ω| = 0.50 × 6.
Kartica 264
Vprašanje
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Odgovor
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Kartica 265
Vprašanje
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Odgovor
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Kartica 266
Vprašanje
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Odgovor
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Kartica 267
Vprašanje
How does moving mass farther from a rotation axis affect rotational inertia?
Odgovor
It increases rotational inertia strongly. For a point mass, I = mr².
Kartica 268
Vprašanje
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Odgovor
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Kartica 269
Vprašanje
Why must angular displacement be in radians for Δs = rΔθ?
Odgovor
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Kartica 270
Vprašanje
When does a nonzero force produce zero torque about an axis?
Odgovor
When its line of action passes through the axis. The lever arm is then zero.
Kartica 271
Vprašanje
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Odgovor
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Kartica 272
Vprašanje
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Odgovor
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Kartica 273
Vprašanje
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Odgovor
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Kartica 274
Vprašanje
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Odgovor
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Kartica 275
Vprašanje
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Odgovor
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Kartica 276
Vprašanje
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Odgovor
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Kartica 277
Vprašanje
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Odgovor
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Kartica 278
Vprašanje
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Odgovor
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Kartica 279
Vprašanje
What is a rigid body's rotational kinetic energy about a fixed axis?
Odgovor
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Kartica 280
Vprašanje
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Odgovor
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Kartica 281
Vprašanje
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Odgovor
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Kartica 282
Vprašanje
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Odgovor
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Kartica 283
Vprašanje
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Odgovor
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Kartica 284
Vprašanje
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Odgovor
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Kartica 285
Vprašanje
Does angular-momentum conservation require rotational kinetic-energy conservation?
Odgovor
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Kartica 286
Vprašanje
Why do astronauts feel weightless in orbit even though gravity acts on them?
Odgovor
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Kartica 287
Vprašanje
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Odgovor
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Kartica 288
Vprašanje
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Odgovor
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Kartica 289
Vprašanje
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Odgovor
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Kartica 290
Vprašanje
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Odgovor
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Kartica 291
Vprašanje
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Odgovor
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Kartica 292
Vprašanje
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Odgovor
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Kartica 293
Vprašanje
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Odgovor
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Kartica 294
Vprašanje
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Odgovor
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Kartica 295
Vprašanje
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Odgovor
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Kartica 296
Vprašanje
How does rotational kinetic energy change if angular speed doubles at fixed I?
Odgovor
It becomes four times as large. Rotational kinetic energy depends on ω².
Kartica 297
Vprašanje
Why should external torque be evaluated about the same axis used for angular momentum?
Odgovor
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Kartica 298
Vprašanje
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Odgovor
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Kartica 299
Vprašanje
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Odgovor
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Kartica 300
Vprašanje
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Odgovor
v = √(GM/r). Gravity supplies the inward net force.
Kartica 301
Vprašanje
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Odgovor
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Kartica 302
Vprašanje
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Odgovor
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Kartica 303
Vprašanje
Why can't the rolling condition alone prove that friction points uphill or downhill?
Odgovor
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Kartica 304
Vprašanje
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Odgovor
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Kartica 305
Vprašanje
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Odgovor
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Kartica 306
Vprašanje
What makes simple harmonic motion a special kind of periodic motion?
Odgovor
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Kartica 307
Vprašanje
What does the amplitude of an SHM displacement graph represent?
Odgovor
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Kartica 308
Vprašanje
How are period and frequency related?
Odgovor
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Kartica 309
Vprašanje
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Odgovor
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Kartica 310
Vprašanje
For one-dimensional SHM, what is the equilibrium position?
Odgovor
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Kartica 311
Vprašanje
How far apart in phase are displacement and velocity in SHM?
Odgovor
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Kartica 312
Vprašanje
When can a simple pendulum be modeled as SHM?
Odgovor
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Kartica 313
Vprašanje
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Odgovor
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Kartica 314
Vprašanje
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Odgovor
U_s = ½kx². It has the same value at +x and -x.
Kartica 315
Vprašanje
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Odgovor
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Kartica 316
Vprašanje
How does a spring oscillator's period change if k becomes four times as large?
Odgovor
The period is halved. T is proportional to 1/√k.
Kartica 317
Vprašanje
How are acceleration and displacement related along the SHM coordinate?
Odgovor
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Kartica 318
Vprašanje
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Odgovor
E = ½kA². It stays constant when dissipative effects are negligible.
Kartica 319
Vprašanje
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Odgovor
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Kartica 320
Vprašanje
How can frequency be read from an oscillation-versus-time graph?
Odgovor
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Kartica 321
Vprašanje
Why does an ideal mass–spring oscillator exhibit SHM?
Odgovor
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Kartica 322
Vprašanje
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Odgovor
1 J. E = ½(50)(0.20²).
Kartica 323
Vprašanje
At maximum positive displacement in SHM, what are velocity and acceleration?
Odgovor
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
Kartica 324
Vprašanje
How does a spring oscillator's period change if its mass becomes four times as large?
Odgovor
The period doubles. T is proportional to √m.
Kartica 325
Vprašanje
Why isn't uniform circular motion itself one-dimensional SHM?
Odgovor
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
Kartica 326
Vprašanje
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Odgovor
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
Kartica 327
Vprašanje
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Odgovor
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
Kartica 328
Vprašanje
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Odgovor
No within the ideal SHM model. The period depends on system parameters, not amplitude.
Kartica 329
Vprašanje
How is maximum speed related to amplitude and angular frequency in SHM?
Odgovor
v_max = ωA. Maximum speed occurs at equilibrium.
Kartica 330
Vprašanje
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Odgovor
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
Kartica 331
Vprašanje
How far apart in phase are displacement and acceleration in SHM?
Odgovor
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
Kartica 332
Vprašanje
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Odgovor
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
Kartica 333
Vprašanje
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Odgovor
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
Kartica 334
Vprašanje
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Odgovor
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
Kartica 335
Vprašanje
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Odgovor
Both are positive. Motion and restoring acceleration point right toward equilibrium.
Kartica 336
Vprašanje
How does a pendulum's period change if its length becomes nine times as large?
Odgovor
The period triples. T is proportional to √L.
Kartica 337
Vprašanje
If SHM starts at maximum positive displacement, what equation gives its position?
Odgovor
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
Kartica 338
Vprašanje
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Odgovor
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
Kartica 339
Vprašanje
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Odgovor
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
Kartica 340
Vprašanje
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Odgovor
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
Kartica 341
Vprašanje
What makes a substance a fluid?
Odgovor
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
Kartica 342
Vprašanje
What is mass density?
Odgovor
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
Kartica 343
Vprašanje
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Odgovor
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
Kartica 344
Vprašanje
What is volume flow rate?
Odgovor
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
Kartica 345
Vprašanje
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Odgovor
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
Kartica 346
Vprašanje
What conditions support the basic Bernoulli model used here?
Odgovor
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
Kartica 347
Vprašanje
Under the ideal model, how does average density predict whether a free object floats or sinks?
Odgovor
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
Kartica 348
Vprašanje
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Odgovor
Q = Av. This gives the volume crossing a completely filled pipe section per time.
Kartica 349
Vprašanje
How does a static fluid exert force on a surface?
Odgovor
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
Kartica 350
Vprašanje
How does pressure change with depth in a static uniform fluid?
Odgovor
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
Kartica 351
Vprašanje
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Odgovor
F_B = mg. The object's weight equals the weight of the fluid it displaces.
Kartica 352
Vprašanje
What is the continuity equation for steady incompressible flow in one filled pipe?
Odgovor
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
Kartica 353
Vprašanje
Why does a static fluid produce an upward buoyant force?
Odgovor
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
Kartica 354
Vprašanje
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Odgovor
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
Kartica 355
Vprašanje
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Odgovor
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
Kartica 356
Vprašanje
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Odgovor
0.060 m³/s. Q = Av = 0.020×3.
Kartica 357
Vprašanje
What does the slope of a mass-versus-volume graph represent for one uniform material?
Odgovor
Density. Since m = ρV, the line's slope is ρ.
Kartica 358
Vprašanje
How do gauge pressure and absolute pressure differ?
Odgovor
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
Kartica 359
Vprašanje
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Odgovor
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
Kartica 360
Vprašanje
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Odgovor
It doubles. Continuity keeps Av constant.
Kartica 361
Vprašanje
When does a fluid element's velocity change?
Odgovor
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
Kartica 362
Vprašanje
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Odgovor
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
Kartica 363
Vprašanje
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Odgovor
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
Kartica 364
Vprašanje
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Odgovor
It becomes four times as large. Area is proportional to radius squared.
Kartica 365
Vprašanje
What does Pascal's principle say for a confined incompressible fluid at rest?
Odgovor
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
Kartica 366
Vprašanje
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Odgovor
ρg. For known g, the slope can determine fluid density.
Kartica 367
Vprašanje
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Odgovor
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
Kartica 368
Vprašanje
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Odgovor
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
Kartica 369
Vprašanje
What physical quantity does each term in P + ½ρv² + ρgy share?
Odgovor
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
Kartica 370
Vprašanje
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Odgovor
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
Kartica 371
Vprašanje
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Odgovor
0.75, or 75%. Use the density ratio for floating equilibrium.
Kartica 372
Vprašanje
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Odgovor
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
Kartica 373
Vprašanje
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Odgovor
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
Kartica 374
Vprašanje
Why does the same force create more pressure on a smaller area?
Odgovor
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
Kartica 375
Vprašanje
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Odgovor
3.0×10³ kg/m³. Divide mass by volume.
Kartica 376
Vprašanje
What conservation law underlies the continuity equation for incompressible flow?
Odgovor
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
Kartica 377
Vprašanje
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Odgovor
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
Kartica 378
Vprašanje
What is the SI unit of pressure?
Odgovor
The pascal, Pa. One pascal equals 1 N/m².
Kartica 379
Vprašanje
How do pressures compare at the same horizontal level in one connected static fluid?
Odgovor
They are equal. Container shape does not change pressure at a fixed elevation.
Kartica 380
Vprašanje
What does specific gravity compare?
Odgovor
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
Kartica 381
Vprašanje
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Odgovor
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
Kartica 382
Vprašanje
How does the particle model distinguish a fluid from a rigid solid?
Odgovor
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
Kartica 383
Vprašanje
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Odgovor
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
Kartica 384
Vprašanje
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Odgovor
200 N. F_B = ρgV = 1000×10×0.020.
Kartica 385
Vprašanje
Why can a steel ship float even though steel is denser than water?
Odgovor
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
Kartica 386
Vprašanje
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Odgovor
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
Kartica 387
Vprašanje
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Odgovor
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
Kartica 388
Vprašanje
What does incompressible mean in the introductory ideal-fluid model?
Odgovor
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
Kartica 389
Vprašanje
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Odgovor
Pressure is lower at the higher point. P + ρgy remains constant.
Kartica 390
Vprašanje
How can water displacement measure an irregular solid's volume?
Odgovor
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
Kartica 391
Vprašanje
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Odgovor
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
Kartica 392
Vprašanje
How can scale readings in air and water determine buoyant force?
Odgovor
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
Kartica 393
Vprašanje
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Odgovor
30,000 Pa. P_gauge = ρgh = 1000×10×3.
Kartica 394
Vprašanje
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Odgovor
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
Kartica 395
Vprašanje
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Odgovor
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
Kartica 396
Vprašanje
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Odgovor
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
Kartica 397
Vprašanje
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Odgovor
5,000 Pa. P = F/A = 200/0.040.
Kartica 398
Vprašanje
Why doesn't a hydraulic lift multiply energy?
Odgovor
The large-force piston moves a shorter distance. Ideally, input work equals output work.
Kartica 399
Vprašanje
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Odgovor
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
Kartica 400
Vprašanje
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Odgovor
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

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