Unit 5: Torque and Rotational Dynamics
Physics 1 · Unit 5 · Paper 3

Torque and Rotational Dynamics unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 44 terms and is the same for everyone, so a teacher can assign “Unit 5, Paper 3” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 40 min 36 points0/17 attempted
1

Center of gravity and tipping

2

Static equilibrium of a beam

3

A distributed weight acts at the center of mass

4

Torque sign convention

5

Rotational kinematic equations

6

Parallel axis theorem qualitatively

7

Rolling without slipping

8

Why rotational inertia squares the distance

9

Direction of angular velocity

10

Lever arm

11

Sign of torque

12

Why mass distribution matters

Short answer 1. Define or explain: Newton's second law for rotation

3 pts

Short answer 2. Define or explain: Converting revolutions to radians

3 pts

Short answer 3. Define or explain: A force through the pivot makes no torque

3 pts

Short answer 4. Define or explain: Angular acceleration of a pulley with mass

3 pts

Free response

12 pts

A uniform solid disk of mass M and radius R is mounted on a frictionless axle through its center. A light string is wrapped around the rim of the disk, and a constant force of magnitude F is applied to the free end of the string, causing the disk to rotate from rest. The rotational inertia of a uniform disk about its central axis is ½MR². Figure 1 (given) is a graph of the applied force F versus time t: a horizontal line at F₀ from t = 0 to t = T.

A. Describe the graph of the net torque exerted on the disk as a function of time over the interval 0 ≤ t ≤ T, including its shape and value.

B. Starting from Newton’s second law in rotational form, derive an expression for the angular acceleration of the disk in terms of F₀, M, R and physical constants.

C. Describe the graph of the disk’s angular velocity as a function of time over 0 ≤ t ≤ T, including its shape, intercept, and slope.

D. The disk is replaced with a hoop of the same mass M and radius R, whose rotational inertia is MR², and the same force is applied for the same time. Indicate whether the hoop’s final angular velocity is greater than, less than, or equal to the disk’s, and justify your answer.