Question

A coin rests 18.0 cm from the center of a turntable. The coefficient of static friction between the coin and turntable surface is 0.420. The turntable starts from rest at t = 0 and rotates with a constant angular acceleration of 0.650 rad/s2. (a) After 3.00 s, what is the angular velocity of the turntable? b) (b) At what speed will the coin start to slip? c) (c) After what period of time will the coin start to slip on the turntable?

Answer 1

w = alpha t = .65*3 = 1.95 radians/second


friction force = .42 * m * g = 4.12 m

Ac = w^2 R
centripetal force required = m w^2 R

m w^2 R = 4.12 m if slip is outward

Note I am ignoring tangential slip due acceleration, check later

w^2 = 4.12/R = 4.12/.18 = 22.9
w = 4.78 rad/s at spin out

4.78 = alpha t
t = 4.78/.65 = 7.36 seconds

go back and check tangential slip to make sure it is negligible

tangential acceleration = alpha R
= .65 * .18 = .117 meters/s^2
that is tiny compared to g so forget it