A rigid bicycle wheel is mounted on a nearly frictionless axle in a physics laboratory
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A rigid bicycle wheel is mounted on a nearly frictionless axle in a physics laboratory. External torques can be applied to the wheel by pulling on a small cord wrapped around its rim.
The wheel is initially at rest. A student first pulls on the cord so that the wheel experiences a constant clockwise torque for a short time interval. Immediately afterward, the student reverses the direction of the pull and applies an equal-magnitude counter-clockwise torque for twice the amount of time.
Assume the magnitude of each applied torque remains constant during the interval in which it acts.
(a) Describe qualitatively how an angular impulse delivered by an external torque changes the angular momentum of a rigid object. In your description, discuss both magnitude and direction.
(b) Considering only the relative magnitudes and directions of the two applied torques and their durations, predict whether the magnitude of the wheel’s angular momentum after the complete sequence of pulls is greater than, less than, or equal to its initial magnitude. Justify your answer without using numerical calculations.
(c) Sketch a qualitative graph of angular momentum L versus time for the entire process, beginning at t=0 when the first torque starts and ending after the second torque finishes. On your sketch, clearly indicate:
• the sign of the slope during each interval,
• the point in time when the slope changes,
• any intervals where L is constant.
Explain what physical quantity the slope of your graph represents.