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Button on a Rotating Platform

A small button placed on a horizontal rotating platform with diameter \(0.320m\) will revolve with the plate when it is brought up to a speed of \(40rev/min\), provided the button is no more than \(0.150m\) from the axis. What is the coefficient of static friction between button and platform?
Discussion: The button moves in a circle so it has acceleration \(a_{rad}\).
The coefficient of static friction $$ \mu_s=\frac{v^2}{Rg}$$ Expressing \(v\) in terms of the period \(T\), $$ v=\frac{2\pi R}{T}$$ so, $$\mu_s=\frac{4\pi^2R}{T^2g}$$.A platform speed of \(40.0rev/min\) corresponds to a period of \(1.50s\) so $$\mu_s=0.269$$

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