# Chapter 12 - Rotation of a Rigid Body - Exercises and Problems: 28

The disk's angular velocity is 530 rpm.

#### Work Step by Step

We can find the moment of inertia of the disk. $I = \frac{1}{2}MR^2$ $I = \frac{1}{2}(4.0~kg)(0.18~m)^2$ $I = 0.0648~kg~m^2$ We can find the torque exerted by the force. $\tau = r\times F$ $\tau = (0.18~m)(5.0~N)$ $\tau = 0.90~N~m$ We can find the angular acceleration. $\tau = I~\alpha$ $\alpha = \frac{\tau}{I}$ $\alpha = \frac{0.90~N~m}{0.0648~kg~m^2}$ $\alpha = 13.9~rad/s^2$ We can find the angular velocity after 4.0 seconds. $\omega = \omega_0+\alpha ~t$ $\omega = 0+\alpha ~t$ $\omega = (13.9~rad/s^2)(4.0~s)$ $\omega = 55.6~rad/s$ We can convert the angular velocity to units of rpm. $\omega = (55.6~rad/s)(\frac{1~rev}{2\pi~rad})(\frac{60~s}{1~min})$ $\omega = 530~rpm$ The disk's angular velocity is 530 rpm.

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