Finding Acceleration in a Cylinder and Wedge Problem

[kpoconno]

A cylinder of mass m, radius a, rolls down a rough wedge of mass M that is free to slide on a smooth horizontal surface. The wedge angle is $$\Theta$$. What is the acceleration of the wedge?



We are looking at the Lagrangian method in my classical physics class and I just don't know where to start on this problem.

The Attempt at a Solution

 

[Gear300]

There is a conservation of momentum along the x-direction horizontal to the ice surface. Since you could assume the initial x-component velocities to be 0m/s, you would have 0 = Mv_w + mv_c (w for wedge and c for cylinder). Thus v_w = -mv_c/M, and you could take the derivative to find the acceleration. You could obtain the derivative of v_c through analyzing the rotational and translational motion of the cylinder.