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.

De autorul Open Study Contributor

Despre acest pachet

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.

Fișele din acest pachet

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

An orange sphere traces an orbital path between a wave, a rotating disc, and a fluid ripple on a dark grid.

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