Circular Motion with Friction

Question

A small stone rests on the outer edge of a disk which is whirling around at about 28 rotations per minute. The diameter of the disk is .32 m.

 

What is the minimum coefficient of static friction between the disk and the stone required to keep the stone on the disk?

Answer 1

In this problem, the centripetal force is the static friction.

 

μmg = mω²r

 

μ = ω²r/g

 

ω = 28(2π) radians / (60 sec) ≅ 2.932 rad/s

 

r = 0.32/2 m = 0.16 m

 

g = 9.8 m/s²

 

μ = ω²r/g = (2.932)²(0.16)/9.8 ≅ 0.14