What is the coefficient of static friction between the button and the platform?

Question

What is the coefficient of static friction between the button and the platform?

A small button placed on a horizontal rotating platform with diameter 0.324 mwill revolve with the platform when it is brought up to a rotational speed of 36.0rev/min, provided the button is a distance no more than 0.147mfrom the axis. What is the coefficient of static friction between the button and the platform? How far from the axis can the button be placed, without slipping, if the platform rotates at 56.0rev/min?

Explanation / Answer

a) = 42 rev/min = 42 x 2 /60 = 4.40 rad/s

on button,

mg = m2 r

x 9.81 = 4.42 x 0.142

= 0.28

b) = 60 rev/min = 60 x 2 /60 = 6.28 rad/s

mg = m2 r   

0.28 x 9.81 = 6.282 x r

r = 0.070 m

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