Problem # 9 - The semicircular disk having a mass of 10 kg is rotating at  = 4 rad/s at the instant  = 60 . If the coefficient of static friction at A is  s = 0.5, determine if the disk slips at this instant.
See attached file for full problem description.
This is a complex problem and we solve it in 4 stages:
1. Find the center of mass and the moment of inertia
2. Assume no slipping and find angular acceleration
3. Find the acceleration of the center of mass
4. Find the friction and normal force at A and see whether the assumption of no slipping holds.
We are given ω = 0.4 rad/s, θ = 60°, R= 0.4 m.
Since the mass of the semicircle is irrelevant we do not use it, and just write "M" in the formulae. All Calculations are done in SI units (kg, s, m).
The center of mass may be given in your book(s) or lecture notes. However, just in case, you can find its derivation on web page http://members.tripod.com/arilizi/CM_OF_A_SEMI_CIRCLE.htm
The solution determines the disk slip at this instant.