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.

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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.

Tämän pakan kortit

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