Problem $2.(25$ points$)$

For this problem, use FBD and particle kinetics. A small box with a mass of $10$ kg is placed on the inner surface of the conical dish at the radius shown. The coefficient of static friction between the object and the conical surface is $0\mathrm{.}35.$

a$)$ Draw a free body diagram of the box.

b$)$ Calculate the fastest angular velocity $($in rpm$)$ the conical surface can rotate about the vertical axis such that the object does not slip up from the position shown.