Torque and Moment of Inertia

Description

Two identical black masses, m, are hung via massless strings over two pulleys of identical mass M and radius R, but different mass distributions. The bearings in the pulleys are frictionless and the strings do not slip as they unwind from their pulleys. The masses fall with different accelerations as shown in the animation (position is in meters and time is in seconds). The mass in the second simulation hits the floor first.

Question

Which pulley has the greater moment of inertia? 

In which simulation is the torque the greatest?     

Instructor Resources

Reference: See Giancoli-PA: 8-6, Giancoli-SE: 11-5.

Answer a: Simulation 1. Students will get this one correct. Since torque is Ia, and the acceleration of the black masses is related to the angular acceleration of the pulley through the radius, the simulation where the hanging mass has the least acceleration also has the pulley with the greatest moment of inertia.

Answer b: Simulation 1. This one is not so obvious. Since we have just asked a question using the definition of torque being Ia, however most students will again relate the torque to Ia, but because the moments of inertia are unknown, this relationship is not very useful. Instead, torque is also equal to rxF. Since the radii are identical, we must consider the force that causes the acceleration, namely the tension in the string. The mass with the larger acceleration has the smaller tension and therefore Simulation 1 has the greater torque applied to the pulley.

Script Author: Aaron Titus