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Problem 10.10: Two identical masses are hung over two different pulleys

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Two identical black masses, m, are hung via massless strings over two pulleys of identical mass M and radius R, but different mass distributions as shown in the animation (position is given in centimeters and time is given in seconds). The bearings in the pulleys are frictionless, and the strings do not slip as they unwind from their pulleys. Restart.

  1. Which mass has the greater acceleration?
  2. Which pulley has the greater moment of inertia?
  3. Which pulley has the greater tension acting on it?
  4. Which pulley has the greater torque acting on it?

Answer the following in terms of a general formula for either pulley using the following variables:

a (the acceleration of the black mass), g, m, M, and R.

  1. What is the tension in the string?
  2. What is the torque acting on the pulley?
  3. What is the moment of inertia of the pulley? Remember that we do not know the pulley's mass distribution.

Problem authored by Aaron Titus and Mario Belloni.

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