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.

Por Open Study Contributor

Sobre este baralho

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.

Cartões deste baralho

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

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

400 cartões