Unit 5: Torque and Rotational Dynamics
Physics C: Mech · Unit 5 · Paper 1

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 38 terms and is the same for everyone, so a teacher can assign “Unit 5, Paper 1” 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 37 min 34 points0/17 attempted
1

Pulley with mass

2

The rotational kinematic equations

3

Solid disk or cylinder about its axis

4

Torque about different axes

5

Static equilibrium conditions

6

Perpendicular-axis theorem

7

Moment arm

8

Combining translation and rotation

9

Rolling down an incline

10

Equilibrium of a leaning ladder

11

Rod about its center

12

Rolling without slipping

Short answer 1. Define or explain: Moment of inertia of a point mass

3 pts

Short answer 2. Define or explain: Why the axis matters

3 pts

Short answer 3. Define or explain: Falling spool or yo-yo

3 pts

Short answer 4. Define or explain: Relating tangential and angular quantities

3 pts

Free response

10 pts

Students are asked to determine the rotational inertia of a uniform disk that is free to rotate about a fixed horizontal axle through its center. A light string is wrapped around a spool of radius R = 0.050 m attached to the disk, and a hanging block of mass m is attached to the free end. The students release the block from rest and measure its acceleration for several different masses. m (kg) 0.10 0.20 0.30 0.40 0.50 a (m/s²) 1.96 3.27 4.20 4.90 5.44 Friction in the axle is negligible.

A(i). Describe a procedure the students could use to measure the acceleration of the block. A(ii). Describe one step that would reduce experimental uncertainty.

B(i). Derive an expression relating the acceleration of the block to the hanging mass m, the spool radius R, and the rotational inertia I of the disk. B(ii). Indicate what quantities the students should graph on the axes to obtain a straight line usable to determine I.

C(i). Calculate the values to be plotted on each axis. C(ii). Describe the axis labels, with units, and the positions of the plotted points, and describe the best-fit line.

D. Using the best-fit line described in part C, calculate an experimental value for the rotational inertia of the disk.