Two inclined planes on either side of a frictionless pulley have angles theta (30 degrees) and phi (60 degrees). On the theta plane is a circular solid cylinder of mass M (1.2 kg) and radius R (.2 m). It is connected by a weightless rope and over the pulley to the other plane to a black of mass m (3 kg). The coefficients of static and kinetic friction are .8 and .5 respectively. The system is released from rest at time t=0. What is the resulting linear and angular acceleration of the cylinder, and which direction is it moving?
The Attempt at a Solution
Through intuition I'm fairly sure the cylinder will be pulled up the theta plane (as the block is on a much steeper incline, and it is more than double the mass). But I'm not sure how to calculate the accelerations of the cylinder. I've set up the fore-diagrams and I'm guessing you use f=ma to find to linear acceleration? And then how do I get the angular?
Thanks so much in advance!