Finding Acceleration in a Cylinder and Wedge Problem

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The discussion focuses on calculating the acceleration of a wedge when a cylinder rolls down it, utilizing the Lagrangian method in classical physics. The conservation of momentum is applied along the x-direction, leading to the equation 0 = Mvw + mvc, where vw represents the wedge's velocity and vc represents the cylinder's velocity. By differentiating this equation, one can derive the acceleration of the wedge. The analysis also involves considering both rotational and translational motion of the cylinder to find the necessary derivatives.

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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 [tex]\Theta[/tex]. 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.



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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.
 

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