Torque:

$\overline{){\mathbf{\tau}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\times}}{\mathbf{F}}}$

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 = 56 g, radius R = 3.3 cm, and moment of inertia 1/2MR^{2}. 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 = 0.375 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case 1 the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping.

Part (a) What is the moment of inertia I_{cm} about the central axis (i.e. the axis perpendicular to the circular face) of the yoyo, in kq-m^{2}?

Part (b) In both cases shown, what is the magnitude of the torque t exerted by the string about the contact point of the yo-yo with the table, in N.m? Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg-m? (d) What is the magnitude of the linear acceleration of the center of mass of the yoyo the moment the string becomes taut, in m/s2

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