AP Physics C: Mechanics Unit 6 Practice Test

Pick a unit and take a timed, AP^®-style test built only from that unit's questions — with AI feedback on every free-response answer.

unit 1 unit 2 unit 3 unit 4 unit 5 unit 6 unit 7

Energy and Momentum of Rotating Systems

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Two ways to practice unit 6

standard

The exam experience, sized to one unit — timed like the real thing

20 Multiple Choice Questions

40 min

1 FRQ – FRQ 1 – Mathematical Routines

24 min

1 FRQ – FRQ 2 – Translation Between Representations

24 min

Sections run back-to-back with the same directions, timers, and scoring as the real exam

Total: 1 hr 28 min

customizable

Pick your own mix of question types

multiple choice questions

free response questions (choose as many as you want)

FRQ 1 – Mathematical Routines · 24 minFRQ 2 – Translation Between Representations · 24 minFRQ 3 – Experimental Design · 24 minFRQ 4 – Qualitative/Quantitative Translation · 24 min

Total: 40 min

How scoring works: multiple choice is scored instantly, free-response answers get point-by-point AI feedback, and your result is a percentage for this unit — not a projected AP^® score.

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AP Physics C: Mechanics Unit 6 practice questions

Try 10 multiple-choice questions from Unit 6 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

Question 1
A solid sphere of mass $M$ and radius $R$ rotates with angular velocity $\omega$ . If the radius is doubled to $2R$ and the angular velocity is halved to $\omega/2$ while the mass remains constant, what is the new rotational kinetic energy?
It remains the same
It decreases by a factor of 2
It increases by a factor of 2
It increases by a factor of 4
Show answer
Answer: (A)
Analyzing the functional dependence reveals that rotational inertia $I$ scales with $R^2$ (factor of 4) while $\omega^2$ scales with $(1/2)^2$ (factor of 1/4), canceling out to leave energy unchanged.
Question 2
A rotating system with initial rotational kinetic energy $K_0$ decreases its moment of inertia to $I/3$ while conserving angular momentum. What is the new rotational kinetic energy?
$3K_0$
$K_0/3$
$K_0$
$9K_0$
Show answer
Answer: (A)
Using the functional dependence $K = L^2 / 2I$ with constant angular momentum $L$ , reducing $I$ by a factor of 3 increases $K$ by a factor of 3.
Question 3
A solid cylinder of mass $M$ and radius $R$ rolls without slipping with linear speed $v$ . If the radius is doubled to $2R$ while $M$ and $v$ remain constant, how does the rotational kinetic energy change?
It remains the same
It decreases by half
It doubles in value
It quadruples in value
Show answer
Answer: (A)
Substituting $I \propto MR^2$ and $\omega = v/R$ into the energy equation shows that $R^2$ terms cancel, making rotational kinetic energy dependent only on $M$ and $v$ .
Question 4
A flywheel starts from rest under the influence of a constant net torque $\tau$ . If the duration of torque application increases from $t$ to $3t$ , by what factor does the final rotational kinetic energy increase?
Factor of 9
Factor of 3
Factor of 6
Factor of 27
Show answer
Answer: (A)
Connecting impulse and energy reveals that $\omega \propto t$ (since $\alpha$ is constant), so kinetic energy $K \propto \omega^2$ scales with $t^2$ .
Question 5
A rigid body starts from rest and rotates under a constant net torque $\tau$ . If the angular displacement increases from $\theta$ to $4\theta$ , by what factor does the final rotational kinetic energy increase?
Factor of 4
Factor of 2
Factor of 8
Factor of 16
Show answer
Answer: (A)
Applying the work-energy theorem ( $W = \tau\Delta\theta = \Delta K$ ) shows a direct linear functional dependence between angular displacement and kinetic energy.
Question 6
A thin rod of mass $M$ and length $L$ rotates with angular velocity $\omega$ about an axis through its center. If the axis is moved to one end of the rod while $M$ , $L$ , and $\omega$ remain constant, the rotational kinetic energy increases by what factor?
Factor of 4
Factor of 2
Factor of 8
Factor of 12
Show answer
Answer: (A)
Comparing the moments of inertia shows $I_{end} = \frac{1}{3}ML^2$ is four times $I_{center} = \frac{1}{12}ML^2$ , so energy $K \propto I$ increases by a factor of 4.
Question 7
Two point masses $m$ are attached to the ends of a massless rod of length $L$ rotating about its center. If $L$ is doubled and $m$ is halved while angular velocity remains constant, how does the rotational kinetic energy change?
It increases by a factor of 2
It decreases by a factor of 2
It remains the same
It increases by a factor of 4
Show answer
Answer: (A)
Analyzing the inertia $I \propto mR^2$ shows that halving mass ( $\times 1/2$ ) and doubling length ( $\times 4$ ) results in a net factor of 2 for $I$ and thus $K$ .
Question 8
Disk A has moment of inertia $I_0$ and Disk B has moment of inertia $2I_0$ . If both disks have the same rotational kinetic energy, what is the ratio of their angular velocities $\omega_B / \omega_A$ ?
$1/\sqrt{2}$
$1/2$
$1/4$
$1$
Show answer
Answer: (A)
Solving $K_A = K_B$ implies $\frac{1}{2}I_0\omega_A^2 = \frac{1}{2}(2I_0)\omega_B^2$ , leading to the inverse square root relationship $\omega_B/\omega_A = \sqrt{1/2}$ .
Question 9
A star of radius $R$ rotates with angular velocity $\omega$ . If it collapses to radius $R/2$ without losing mass, what is its new rotational kinetic energy in terms of the initial energy $K_0$ ?
$4K_0$
$K_0/4$
$K_0/2$
$2K_0$
Show answer
Answer: (A)
Combining conservation of angular momentum ( $L$ is constant) with the change in inertia ( $I \propto R^2 \rightarrow I/4$ ) means $K = L^2/2I$ increases by a factor of 4.
Question 10
A hoop ( $I=MR^2$ ) and a uniform disk ( $I=\frac{1}{2}MR^2$ ) of equal mass and radius roll down the same incline from rest. What is the ratio of the hoop's final rotational kinetic energy to the disk's final rotational kinetic energy?
$3/2$
$2/3$
$1$
$4/3$
Show answer
Answer: (A)
Using energy conservation, the hoop converts 1/2 of potential energy to rotation while the disk converts 1/3, yielding a ratio of $(1/2)/(1/3) = 3/2$ .

What's on the AP Physics C: Mechanics Unit 6 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

20 Multiple Choice Questions (40 minutes)
1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

Questions are drawn from 1365 multiple-choice questions and 20 FRQs written for Unit 6, Energy and Momentum of Rotating Systems.

Practice AP Physics C: Mechanics Unit 6 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

FRQ 1 – Mathematical Routines (6 questions)
FRQ 2 – Translation Between Representations (4 questions)
FRQ 3 – Experimental Design (5 questions)
FRQ 4 – Qualitative/Quantitative Translation (5 questions)

AP Physics C: Mechanics Unit 6 Practice Test

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AP Physics C: Mechanics Unit 6 practice questions

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