A horizontal stick of mass m has its left end attached to a pivot on a plane inclined at an angle theta, while its right end rest on top of a cylinder also of mass m which in turn rests on the plane as shown. The coefficients of friction at both points is (mu).
Sorry I couldn't add the symbols for some reason. I am always having problems attaching the drawing. Hopefully I can fix this after I post.
a.) Assuming the system is at rest, what is the normal force from the plane on the cylinder?
b.) What is the smallest value of (mu) in terms of theta for which the system does not slip?
The Attempt at a Solution
For a.) the force on the cylinder from the stick is just mg/2 and the force of gravity from the ball is just mg. Then the normal force on the ball from the plane must be (mg/2+mg)cos(theta) = 1.5mg*cos(theta). Hopefully I'm right up to that point.
For part b.) do I need I need to use torques? I did not so I think I may be wrong. I just solved (mu)1.5mg*cos(theta) + (mu)0.5mg*cos(theta) >= 1.5mg*sin(theta) and got (mu) >= 3/4 * tan(theta)
Can someone let me know if I did this correctly or if I need to implement torques? Any help would be great.