A thin solid disk of radius 0.25 m is mounted on a nearly frictionless vertical axle…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A thin solid disk of radius 0.25 m is mounted on a nearly frictionless vertical axle through its center. At time t = 0 the disk is rotating at 6.0 rad/s counter-clockwise. A small electric motor delivers a constant external torque of 4.0 N·m to the disk in the clockwise direction for the time interval 0 ≤ t ≤ 4.0 s. Immediately afterward, the motor is switched off and no appreciable external torque acts on the disk.
Assume the disk’s mass distribution does not change at any time.
(a) Describe qualitatively how the angular momentum of the disk changes during the 4.0 s interval while the motor is operating and during the subsequent interval when the motor is off.
(b) Explain the relationship between the external torque exerted by the motor and the change in the disk’s angular momentum over the operating interval.
(c) Suppose instead the motor delivered a torque of 8.0 N·m for only 2.0 s. Compare the magnitude and direction of the resulting change in angular momentum with that found in part (a), and justify your answer without performing explicit numerical calculations.