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.

Autor Open Study Contributor

O tej talii

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.

Karty w tej talii

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

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