# A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. Find the acceleration of the wedge and the acceleration of the sphere relative to the wedge. I have written out the equations of motion for the sphere and the wedge and also the equation of motion for the rotational motion of the sphere. But then I get stuck. I don't know how I should relate the angular accleration $\alpha$ of the sphere with the acclerations $a_{\perp},a_{\parallel}$ appearing in its equations of motion. Can anyone please help me out? Thanks!

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