---
title: "AP Physics C: Mechanics Unit 6 Practice Test"
description: "A timed AP Physics C: Mechanics Unit 6 (Energy and Momentum of Rotating Systems) practice test in the AP format, drawn from 1,365 multiple-choice questions and 20 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-c-mechanics/unit-test/6"
type: "unit-test"
subject: "AP Physics C: Mechanics"
unit: "Unit 6"
---

# AP Physics C: Mechanics Unit 6 Practice Test

## Overview

A timed AP Physics C: Mechanics Unit 6 (Energy and Momentum of Rotating Systems) practice test in the AP format, drawn from 1,365 multiple-choice questions and 20 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

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

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-c-mechanics/frqs/mathematical-routines?unit=6): 6 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-c-mechanics/frqs/translation-between-representations?unit=6): 4 questions
- [FRQ 3 – Experimental Design](/ap-physics-c-mechanics/frqs/experimental-design?unit=6): 5 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-c-mechanics/frqs/qualitative-quantitative-translation?unit=6): 5 questions

## Practice Questions

### 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?

- (A) It remains the same
- (B) It decreases by a factor of 2
- (C) It increases by a factor of 2
- (D) It increases by a factor of 4

**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?

- (A) $$3K_0$$
- (B) $$K_0/3$$
- (C) $$K_0$$
- (D) $$9K_0$$

**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?

- (A) It remains the same
- (B) It decreases by half
- (C) It doubles in value
- (D) It quadruples in value

**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?

- (A) Factor of 9
- (B) Factor of 3
- (C) Factor of 6
- (D) Factor of 27

**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?

- (A) Factor of 4
- (B) Factor of 2
- (C) Factor of 8
- (D) Factor of 16

**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?

- (A) Factor of 4
- (B) Factor of 2
- (C) Factor of 8
- (D) Factor of 12

**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?

- (A) It increases by a factor of 2
- (B) It decreases by a factor of 2
- (C) It remains the same
- (D) It increases by a factor of 4

**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 $$\omega_B / \omega_A$$?

- (A) $$1/\sqrt{2}$$
- (B) $$1/2$$
- (C) $$1/4$$
- (D) $$1$$

**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 $$K_0$$?

- (A) $$4K_0$$
- (B) $$K_0/4$$
- (C) $$K_0/2$$
- (D) $$2K_0$$

**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?

- (A) $$3/2$$
- (B) $$2/3$$
- (C) $$1$$
- (D) $$4/3$$

**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 $$(1/2)/(1/3) = 3/2$$.

## Review the Unit

- [6.1 Rotational Kinetic Energy](/ap-physics-c-mechanics/unit-6/1-rotational-kinetic-energy/study-guide/Y5pLDWQTbxH05tCF)
- [6.2 Torque and Work](/ap-physics-c-mechanics/unit-6/2-torque-and-work/study-guide/IDr6scmUlLJQ3Uub)
- [6.3 Angular Momentum and Angular Impulse](/ap-physics-c-mechanics/unit-6/3-angular-momentum-and-angular-impulse/study-guide/3jrKVVLAakxu58LX)
- [6.4 Conservation of Angular Momentum](/ap-physics-c-mechanics/unit-6/4-conservation-of-angular-momentum/study-guide/9JJXeFccr7Xo7FHS)
- [6.5 Kinetic Energy of a System with Translational and Rotational Motion](/ap-physics-c-mechanics/unit-6/5-kinetic-energy-of-a-system-with-translational-and-rotational-motion/study-guide/tpS8vdLgJ6AQpm2V)
- [6.6 Motion of Orbiting Satellites](/ap-physics-c-mechanics/unit-6/6-motion-of-orbiting-satellites/study-guide/nmLPsSq9JDXcENSW)

## Other Unit Tests

- [Unit 1: Kinematics](/ap-physics-c-mechanics/unit-test/1)
- [Unit 2: Force and Translational Dynamics](/ap-physics-c-mechanics/unit-test/2)
- [Unit 3: Work, Energy, and Power](/ap-physics-c-mechanics/unit-test/3)
- [Unit 4: Linear Momentum](/ap-physics-c-mechanics/unit-test/4)
- [Unit 5: Torque and Rotational Dynamics](/ap-physics-c-mechanics/unit-test/5)
- [Unit 7: Oscillations](/ap-physics-c-mechanics/unit-test/7)

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