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.

מאת Open Study Contributor

ללמוד את החפיסה הזו בחינם

Nibomo תיפתח כדי שתוכל להתחיל ללמוד.

פרטי החפיסה

כרטיסים: 400 כרטיסים
גרסה: 3
פורסם: 26 באוגוסט 2026
עודכן לאחרונה: 10 בספטמבר 2026
רישיון: Common knowledge · CC0 1.0
שפות הקהל: en
נושא: Physics
רמה: AP Physics 1
תגיות: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

חפיסות דומות

על החפיסה הזו

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.

הכרטיסים בחפיסה הזו

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