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.

Szerző Open Study Contributor

A pakliról

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.

Kártyák ebben a pakliban

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