cient of friction between the yoyo and the tabletop is μ. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. a. Develop an expression for the moment of inertia ICM about the central axis of the yoyo in terms of the given quantities and fundamental constants.
A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M, radius R, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F. The coefficient of friction between the yoyo and the tabletop is μ. The tension in the string is not sufficient to cause the yoyo to leave the tabletop.
a. Develop an expression for the moment of inertia ICM about the central axis of the yoyo in terms of the given quantities and fundamental constants.
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b. Determine an expression for the magnitude of the torque τ exerted by the string about the contact point of the yo-yo with the table. τ =
c. Develop an expression for the moment of inertia of the yo-yo about the contact point with the table. I =
d. Determine the magnitude of the linear acceleration of the center of mass of the yoyo the moment the string becomes taught.
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