---
title: "AP Physics 1 Unit 5 Practice Test"
description: "A timed AP Physics 1 Unit 5 (Torque and Rotational Dynamics) practice test in the AP format, drawn from 1,322 multiple-choice questions and 30 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-1-revised/unit-test/5"
type: "unit-test"
subject: "AP Physics 1"
unit: "Unit 5"
---

# AP Physics 1 Unit 5 Practice Test

## Overview

A timed AP Physics 1 Unit 5 (Torque and Rotational Dynamics) practice test in the AP format, drawn from 1,322 multiple-choice questions and 30 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=5): 3 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-1-revised/frqs/translation-between-representations?unit=5): 5 questions
- [FRQ 3 – Experimental Design](/ap-physics-1-revised/frqs/experimental-design?unit=5): 8 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-1-revised/frqs/qualitative-quantitative-translation?unit=5): 14 questions

## Practice Questions

### Question 1

A force $$F$$ is applied to one end of a rod of length $$L$$ at an angle $$\theta$$ relative to the rod. The rod is pivoted at the other end. Which expression gives the magnitude of the torque exerted on the rod about the pivot?

- (A) $$FL\sin\theta$$
- (B) $$FL\cos\theta$$
- (C) $$\frac{F\sin\theta}{L}$$
- (D) $$\frac{F\cos\theta}{L}$$

**Answer: (A)** Torque is defined as the cross product $$\tau = rF\sin\theta$$. Here $$r=L$$, so the magnitude is $$FL\sin\theta$$, representing the perpendicular component of force.

### Question 2

A ladder leans against a smooth wall, with its base on rough ground. In Position A, the ladder makes an angle of $$75^\circ$$ with the ground. In Position B, the base is moved further out so the angle is $$60^\circ$$. The ladder remains stationary in both positions. How does the static friction force at the base in Position B compare to Position A?

- (A) It is greater, to balance the increased torque from gravity
- (B) It is greater, to balance the increased normal force from the ground
- (C) It is smaller, because the ladder is closer to being horizontal
- (D) It is smaller, because the normal force from the wall decreases

**Answer: (A)** Analyzing torque equilibrium shows that as the angle decreases, the lever arm for gravity increases, requiring a larger normal force from the wall to prevent rotation. Static friction at the base must balance this increased wall force.

### Question 3

A flywheel initially rotating at $$12.0 \text{ rad/s}$$ slows down with a constant angular acceleration of $$-2.0 \text{ rad/s}^2$$. What is the total angular displacement of the flywheel from the moment it begins to slow down until it comes to a complete stop?

- (A) $$6.0 \text{ rad}$$
- (B) $$36 \text{ rad}$$
- (C) $$72 \text{ rad}$$
- (D) $$144 \text{ rad}$$

**Answer: (B)** Using $$\omega^2 = \omega_0^2 + 2\alpha\Delta\theta$$, substitute values: $$0 = (12)^2 + 2(-2)\Delta\theta$$. Solving gives $$144 = 4\Delta\theta$$, so $$\Delta\theta = 36 \text{ rad}$$.

### Question 4

A car with tires of radius $$0.25 \text{ m}$$ accelerates from rest with a constant linear acceleration of $$2.0 \text{ m/s}^2$$. Assuming the tires roll without slipping, what is their angular velocity after $$4.0 \text{ s}$$?

- (A) $$2.0 \text{ rad/s}$$
- (B) $$8.0 \text{ rad/s}$$
- (C) $$16 \text{ rad/s}$$
- (D) $$32 \text{ rad/s}$$

**Answer: (D)** First, find linear velocity: $$v = at = 2(4) = 8 \text{ m/s}$$. Then convert to angular velocity using $$v = r\omega$$: $$\omega = 8 / 0.25 = 32 \text{ rad/s}$$.

### Question 5

A fan blade accelerates from rest with a constant angular acceleration of $$\pi \text{ rad/s}^2$$. How many revolutions does the blade complete in the first $$4.0 \text{ s}$$ of motion?

- (A) $$2.0 \text{ revolutions}$$
- (B) $$4.0 \text{ revolutions}$$
- (C) $$8.0 \text{ revolutions}$$
- (D) $$16 \text{ revolutions}$$

**Answer: (B)** Calculate displacement in radians: $$\Delta\theta = \frac{1}{2}\alpha t^2 = 0.5(\pi)(16) = 8\pi \text{ rad}$$. Convert to revolutions: $$8\pi / 2\pi = 4.0 \text{ revolutions}$$.

### Question 6

A disk rotating at $$4.0 \text{ rad/s}$$ accelerates constantly to $$12 \text{ rad/s}$$ while rotating through an angular displacement of $$32 \text{ rad}$$. What is the angular acceleration of the disk?

- (A) $$1.0 \text{ rad/s}^2$$
- (B) $$2.0 \text{ rad/s}^2$$
- (C) $$4.0 \text{ rad/s}^2$$
- (D) $$8.0 \text{ rad/s}^2$$

**Answer: (B)** Use $$\omega^2 = \omega_0^2 + 2\alpha\Delta\theta$$: $$144 = 16 + 2\alpha(32)$$. Simplify to $$128 = 64\alpha$$, so $$\alpha = 2.0 \text{ rad/s}^2$$.

### Question 7

A string is wrapped around a pulley of radius $$0.20 \text{ m}$$. A block attached to the string falls from rest, causing the pulley to rotate. If the block falls $$5.0 \text{ m}$$ in $$2.0 \text{ s}$$, what is the average angular acceleration of the pulley?

- (A) $$2.5 \text{ rad/s}^2$$
- (B) $$6.25 \text{ rad/s}^2$$
- (C) $$12.5 \text{ rad/s}^2$$
- (D) $$25 \text{ rad/s}^2$$

**Answer: (C)** First find linear acceleration: $$y = \frac{1}{2}at^2 \rightarrow 5 = 0.5a(4) \rightarrow a = 2.5 \text{ m/s}^2$$. Then convert: $$\alpha = a/r = 2.5/0.2 = 12.5 \text{ rad/s}^2$$.

### Question 8

A rotor starts from rest and accelerates at $$3.0 \text{ rad/s}^2$$ for $$4.0 \text{ s}$$, then continues at constant angular velocity for another $$4.0 \text{ s}$$. What is the total angular displacement?

- (A) $$48 \text{ rad}$$
- (B) $$72 \text{ rad}$$
- (C) $$96 \text{ rad}$$
- (D) $$144 \text{ rad}$$

**Answer: (B)** Phase 1: $$\theta_1 = 0.5(3)(4^2) = 24 \text{ rad}$$. Final speed $$\omega = 3(4) = 12 \text{ rad/s}$$. Phase 2: $$\theta_2 = 12(4) = 48 \text{ rad}$$. Total = $$24 + 48 = 72 \text{ rad}$$.

### Question 9

A wheel is initially rotating counterclockwise at $$8.0 \text{ rad/s}$$. It is subjected to a constant clockwise angular acceleration of $$2.0 \text{ rad/s}^2$$. What is the angular displacement of the wheel after $$5.0 \text{ s}$$?

- (A) $$15 \text{ rad}$$
- (B) $$25 \text{ rad}$$
- (C) $$40 \text{ rad}$$
- (D) $$65 \text{ rad}$$

**Answer: (A)** Define CCW as positive. $$\theta = \omega_0 t + \frac{1}{2}\alpha t^2$$. Substitute: $$8(5) + 0.5(-2)(25) = 40 - 25 = 15 \text{ rad}$$.

### Question 10

An object's angular velocity as a function of time is given by $$\omega(t) = 4.0 + 2.0t$$, where $$\omega$$ is in rad/s and $$t$$ is in seconds. What is the angular displacement of the object from $$t=0$$ to $$t=3.0 \text{ s}$$?

- (A) $$10 \text{ rad}$$
- (B) $$15 \text{ rad}$$
- (C) $$21 \text{ rad}$$
- (D) $$30 \text{ rad}$$

**Answer: (C)** Displacement is the area under the $$\omega-t$$ graph (trapezoid). $$\omega_0=4$$, $$\omega_3=10$$. Area = $$\frac{4+10}{2} \times 3 = 7 \times 3 = 21 \text{ rad}$$.

## Review the Unit

- [5.1 Rotational Kinematics](/ap-physics-1-revised/unit-5/1-rotational-kinematics/study-guide/jxNgrZLunMqFLWMW)
- [5.2 Connecting Linear and Rotational Motion](/ap-physics-1-revised/unit-5/2-connecting-linear-and-rotational-motion/study-guide/mEh5fraXXhGnwvpz)
- [5.3 Torque](/ap-physics-1-revised/unit-5/3-torque/study-guide/I9b5y8FshkMfALc5)
- [5.4 Rotational Inertia](/ap-physics-1-revised/unit-5/4-rotational-inertia/study-guide/DTC3EVaSpnS57xK2)
- [5.5 Rotational Equilibrium and Newton's First Law in Rotational Form](/ap-physics-1-revised/unit-5/5-rotational-equilibrium-and-newtons-first-law-in-rotational-form/study-guide/TogHn1BiaEEPvaXR)
- [5.6 Newton's Second Law in Rotational Form](/ap-physics-1-revised/unit-5/6-newtons-second-law-in-rotational-form/study-guide/TfwjbrsZ50b28wJ7)

## 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 6: Rotating Systems: Energy & Momentum](/ap-physics-1-revised/unit-test/6)
- [Unit 7: Oscillations](/ap-physics-1-revised/unit-test/7)
- [Unit 8: Fluids](/ap-physics-1-revised/unit-test/8)

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