---
title: "AP Physics 1 Unit 6 Practice Test"
description: "A timed AP Physics 1 Unit 6 (Rotating Systems: Energy & Momentum) practice test in the AP format, drawn from 1,589 multiple-choice questions and 34 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-1-revised/unit-test/6"
type: "unit-test"
subject: "AP Physics 1"
unit: "Unit 6"
---

# AP Physics 1 Unit 6 Practice Test

## Overview

A timed AP Physics 1 Unit 6 (Rotating Systems: Energy & Momentum) practice test in the AP format, drawn from 1,589 multiple-choice questions and 34 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-1-revised/frqs/mathematical-routines?unit=6): 6 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-1-revised/frqs/translation-between-representations?unit=6): 1 question
- [FRQ 3 – Experimental Design](/ap-physics-1-revised/frqs/experimental-design?unit=6): 9 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-1-revised/frqs/qualitative-quantitative-translation?unit=6): 18 questions

## Practice Questions

### Question 1

A rotating star of mass M and radius R collapses to a final radius of R/2 due to internal gravitational forces. Assuming the star remains spherical, loses no mass, and is not acted upon by external torques, how do the final angular momentum L_f and final angular velocity w_f compare to the initial values?

- (A) L_f is equal to L_i; w_f is 4 times w_i
- (B) L_f is equal to L_i; w_f is 2 times w_i
- (C) L_f is 1/4 of L_i; w_f is equal to w_i
- (D) L_f is 1/2 of L_i; w_f is 2 times w_i

**Answer: (A)** Connecting conservation of angular momentum with changes in rotational inertia reveals the system's behavior. Since no external torques act on the star, L remains constant. Rotational inertia I is proportional to R^2, so halving the radius reduces I to (1/2)^2 = 1/4 of its initial value. To conserve L (where L = Iw), w must increase by a factor of 4.

### Question 2

A uniform rod is pivoted at one end. In Trial 1, a clay lump strikes the rod's free end and sticks. In Trial 2, a rubber ball of identical mass and velocity strikes the free end and bounces backward. Compare the change in the rod's angular momentum (dL_rod) and the total angular momentum of the system (dL_sys) immediately after the collision.

- (A) dL_rod is greater in Trial 2; dL_sys is conserved in both
- (B) dL_rod is greater in Trial 1; dL_sys is conserved in both
- (C) dL_rod is equal in both trials; dL_sys decreases in Trial 1
- (D) dL_rod is equal in both trials; dL_sys decreases in Trial 2

**Answer: (A)** Analyzing the impulse transfer and system boundaries distinguishes the two outcomes. The bouncing ball delivers a greater impulse (change in momentum from +p to -p) than the sticking clay (+p to 0), causing a larger change in the rod's angular momentum. However, for the system (rod + object), net external torque is zero, so total angular momentum is conserved in both trials.

### Question 3

Satellite A orbits Earth at radius R, while Satellite B orbits at radius 4R. Both satellites have the same mass and move in circular orbits. How do the angular momentum L and kinetic energy K of Satellite B compare to those of Satellite A?

- (A) L_B is 2 times L_A; K_B is 1/4 times K_A
- (B) L_B is 4 times L_A; K_B is 1/4 times K_A
- (C) L_B is 2 times L_A; K_B is 1/2 times K_A
- (D) L_B is 4 times L_A; K_B is 1/2 times K_A

**Answer: (A)** Combining orbital mechanics with definitions of L and K reveals the scaling relationships. Orbital speed v scales with 1/sqrt(r), so v_B is half of v_A. Angular momentum L = mvr scales with sqrt(r), making L_B double L_A. Kinetic energy K scales with v^2 (and thus 1/r), making K_B one-fourth of K_A.

### Question 4

A hollow sphere and a solid sphere have equal mass M and radius R. Both rotate about an axis through their centers with the same angular speed w. Compare the magnitude of the angular momentum L and the rotational kinetic energy K of the hollow sphere to those of the solid sphere.

- (A) L is greater and K is greater for the hollow sphere
- (B) L is equal and K is equal for both spheres
- (C) L is equal and K is greater for the hollow sphere
- (D) L is greater and K is equal for the hollow sphere

**Answer: (A)** Evaluating how mass distribution affects rotational inertia determines the comparison. A hollow sphere has mass concentrated further from the axis than a solid sphere, giving it a larger rotational inertia I. Since L = Iw and K = 0.5Iw^2, and w is identical for both, the hollow sphere has greater L and K.

### Question 5

A satellite moves in a circular orbit of radius $$R$$ and has angular momentum $$L$$. If the satellite is moved to a circular orbit of radius $$4R$$, what is the new angular momentum of the satellite?

- (A) $$2L$$
- (B) $$4L$$
- (C) $$L/2$$
- (D) $$16L$$

**Answer: (A)** Angular momentum is $$L = mvr$$. Since $$v \propto 1/\sqrt{r}$$, $$L \propto r(1/\sqrt{r}) = \sqrt{r}$$. Increasing $$r$$ by a factor of 4 increases $$L$$ by a factor of $$\sqrt{4} = 2$$.

### Question 6

A satellite in a circular orbit of radius $$R$$ has kinetic energy $$K$$. If the satellite is moved to a circular orbit of radius $$2R$$, what is the new kinetic energy?

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

**Answer: (A)** Kinetic energy is $$K = \frac{1}{2}mv^2$$. Since $$v = \sqrt{GM/R}$$, $$v^2 \propto 1/R$$, and thus $$K \propto 1/R$$. Doubling the radius halves the kinetic energy.

### Question 7

A flywheel with rotational inertia $$I$$ spins with angular velocity $$\omega$$. If the angular velocity is increased to $$3\omega$$ while the rotational inertia remains constant, what is the new rotational kinetic energy in terms of the initial energy $$K$$?

- (A) It increases to nine times the initial kinetic energy.
- (B) It increases to three times the initial kinetic energy.
- (C) It increases to six times the initial kinetic energy.
- (D) It increases to twenty-seven times the initial kinetic energy.

**Answer: (A)** Rotational kinetic energy depends on the square of the angular velocity ($$K = \frac{1}{2}I\omega^2$$). Tripling the angular velocity results in a factor of $$3^2 = 9$$ increase in energy.

### Question 8

Sphere A has radius $$R$$ and mass $$M$$. Sphere B has radius $$2R$$ and mass $$M$$. If both solid spheres spin at the same angular velocity $$\omega$$, how does the rotational kinetic energy of Sphere B compare to that of Sphere A?

- (A) It is four times the kinetic energy of Sphere A.
- (B) It is two times the kinetic energy of Sphere A.
- (C) It is eight times the kinetic energy of Sphere A.
- (D) It is sixteen times the kinetic energy of Sphere A.

**Answer: (A)** Rotational inertia for a sphere is proportional to the square of the radius ($$I \propto R^2$$). Doubling the radius quadruples $$I$$, which linearly quadruples the kinetic energy ($$K \propto I$$).

### Question 9

An isolated collapsing star's radius decreases to half its original value ($$R_{new} = R/2$$) while its mass remains constant. If angular momentum is conserved, how does the star's new rotational kinetic energy compare to its initial value?

- (A) It increases by a factor of four due to conservation.
- (B) It increases by a factor of two due to conservation.
- (C) It decreases by a factor of two due to inertia changes.
- (D) It decreases by a factor of four due to inertia changes.

**Answer: (A)** Rotational inertia decreases by a factor of 4 ($$I \propto R^2$$). Since angular momentum $$L$$ is conserved, $$K = \frac{L^2}{2I}$$ increases by a factor of 4 (inverse relationship with $$I$$).

### Question 10

A solid cylinder of mass $$M$$ and radius $$R$$ rolls without slipping at linear speed $$v$$. A second cylinder of mass $$M$$ and radius $$2R$$ rolls without slipping at the same linear speed $$v$$. How does the rotational kinetic energy of the second cylinder compare to the first?

- (A) It remains equal to the initial rotational kinetic energy.
- (B) It becomes half of the initial rotational kinetic energy.
- (C) It becomes twice the initial rotational kinetic energy.
- (D) It becomes four times the initial rotational kinetic energy.

**Answer: (A)** Rotational kinetic energy for a rolling object is $$K = \frac{1}{2}I\omega^2 = \frac{1}{2}(cMR^2)(v/R)^2 = \frac{1}{2}cMv^2$$. The radius $$R$$ cancels out, so energy depends only on mass and linear speed.

## Review the Unit

- [6.1 Rotational Kinetic Energy](/ap-physics-1-revised/unit-6/1-rotational-kinetic-energy/study-guide/OM0z7GYjhkcWoIlZ)
- [6.2 Torque and Work](/ap-physics-1-revised/unit-6/2-torque-and-work/study-guide/D8FrXUDk7DwXDsEZ)
- [6.3 Angular Momentum and Angular Impulse](/ap-physics-1-revised/unit-6/3-angular-momentum-and-angular-impulse/study-guide/SSARCXdw55Twhoxd)
- [6.4 Conservation of Angular Momentum](/ap-physics-1-revised/unit-6/4-conservation-of-angular-momentum/study-guide/uWUv9Ei9tpPYbvI9)
- [6.5 Rolling](/ap-physics-1-revised/unit-6/5-rolling/study-guide/Ezw0DtDmEDYrpqzr)
- [6.6 Motion of Orbiting Satellites](/ap-physics-1-revised/unit-6/6-motion-of-orbiting-satellites/study-guide/tzB1DCcspZo8vXIC)

## Other Unit Tests

- [Unit 1: Kinematics](/ap-physics-1-revised/unit-test/1)
- [Unit 2: Force and Translational Dynamics](/ap-physics-1-revised/unit-test/2)
- [Unit 3: Work, Energy, and Power](/ap-physics-1-revised/unit-test/3)
- [Unit 4: Linear Momentum](/ap-physics-1-revised/unit-test/4)
- [Unit 5: Torque and Rotational Dynamics](/ap-physics-1-revised/unit-test/5)
- [Unit 7: Oscillations](/ap-physics-1-revised/unit-test/7)
- [Unit 8: Fluids](/ap-physics-1-revised/unit-test/8)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)