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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 $$\mu_s=0.269$$

July 29, 2017