A student investigates the rotational motion of a thin
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student investigates the rotational motion of a thin, uniform disk mounted on a nearly frictionless axle. A torque sensor records the net external torque acting on the disk for the first 6 s after the disk is released from rest.
• From t = 0 s to t = 2 s the sensor reads a constant +3.0 N·m.
• From t = 2 s to t = 4 s the reading gradually decreases linearly to 0 N·m at t = 4 s.
• From t = 4 s to t = 6 s the sensor reads a constant −2.0 N·m.
Positive torque corresponds to counter-clockwise (ccw) rotation; negative torque corresponds to clockwise (cw) rotation.
(a) Identify the time interval(s) during which the net external torque on the disk is ccw and the interval(s) during which it is cw.
(b) Describe, without performing numerical calculations, how the reading of the torque sensor during any time interval is related to the change in the disk’s angular momentum during that same interval.
(c) The disk starts from rest at t = 0 s. Explain whether the disk’s angular speed is increasing or decreasing, and whether it is rotating ccw or cw, at (i) t = 3 s and (ii) t = 5 s.
(d) Suppose the area enclosed by the torque-versus-time curve from 0 s to 2 s is equal in magnitude but opposite in sign to the area from 4 s to 6 s. Explain what the equality of these two areas implies about the disk’s angular momentum at t = 6 s.