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.

Door Open Study Contributor

Over dit deck

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.

Kaarten in dit deck

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