# Chapter 5 - Problems - Page 190: 83

The coin will not slide off the turntable as long as the coin is placed within $8.05~cm$ from the center of the turntable.

#### Work Step by Step

The angular speed is $(33.3~rpm)(2\pi~rad/rev)(1~min/60~s) = 3.49~rad/s$ For a given angular speed, the force of friction can provide the required centripetal force to keep the coin moving in a circle as long as the radius of rotation is small enough. We can find the radius when the force of static friction reaches its maximum possible value: $F_f = m~a_r$ $mg~\mu_s = m~\omega^2~r$ $r = \frac{g~\mu_s}{\omega^2}$ $r = \frac{(9.80~m/s^2)(0.10)}{(3.49~rad/s)^2}$ $r = 0.0805~m$ $r = 8.05~cm$ The coin will not slide off the turntable as long as the coin is placed within $8.05~cm$ from the center of the turntable.

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