Question

A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk?

A) Pulling on the cord, exerting a force of 15N for 2s and then 25N for 3s, and measuring the final angular velocity of the disk.
B) For five different time intervals, pulling on the cord, exerting a force of 15N, and then measuring the angle through which the disk rotates in each case.
C) For five different time intervals, pulling on the cord, and then measuring the final angular velocity of the disk.
D) For five forces of different magnitude, pulling on the cord for 5s, and then measuring the final angular velocity of the disk.

Answer 1

(D) Γ = I α expresses relationship between torque and angular acceleration for a fixed moment of inertia

F * R = Γ will provide the applied torque for (D)

If one knows the final angular velocity then α can be computed for the time period of 5 s

Plotting the torque vs the angular acceleration will provide the slope of the line which is the moment of inertia