# Cylinder and Wedge problem?

1. Oct 28, 2009

### 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.

3. The attempt at a solution

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2. Oct 28, 2009

### 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 = Mvw + mvc (w for wedge and c for cylinder). Thus vw = -mvc/M, and you could take the derivative to find the acceleration. You could obtain the derivative of vc through analyzing the rotational and translational motion of the cylinder.