Week 14 (Nov. 11 - 15)

Reading: PSE Chap 11, Rolling motion, angular momentum and torque
Topics: torque, rotational dynamics.


Homework Problems:

  1. Rotational inertia of triangle: Three 1 kg masses are fixed at the corners of an equilateral triangle. The sides have length 2 meters. If this triangular system rotates around the center of mass of the triangle, then what is its rotational inertia? Here is a video solution.
  2. One mass suspended from pulley: A 10 kg mass is suspended from a thin string. The string is wrapped a bunch of times around a solid disk that acts as a pulley. The disk/pulley has a mass of 2 kg and a diameter of 5 cm. The mass is released from rest and so it begins to descend due to its weight. As it does so, the string, which is wrapped around the disk, causes the disk to rotate (the string does not slip). Note: here is a video solution.
    • How much torque does the 10 kg mass exert on the disk?
    • What is the angular acceleration of the pulley as the 10 kg mass falls? Is it constant?
    • What is the angular velocity of the pulley? Is it constant, or time dependent?
    • The floor is 3 meters beneath the release point of the 10 kg mass. How long does it take to hit the floor?
    • What is the speed of the mass just before it hits the floor?
  3. Two masses suspended from pulley: Suppose that, like in the previous problem, the 10 kg mass is suspended from a string which is wrapped a bunch of times round the disk/pulley. But now suppose the other end of the string is attached to another (3 kg) mass suspended from the pulley. So as the 10 kg mass falls, the 3 kg mass rises. Repeat the previous problem. Here is a video solution.

Quiz: Monday Nov. 13. Covering rotational kinematics.
General College Physics