Rolling Body mechanics

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1. Aug 5, 2017

Carbon123

1. The problem statement, all variables and given/known data
In the picture ,problem 8.29

2. Relevant equations
Energy conservation ,velocity relation ,momentum

3. The attempt at a solution
First i defined the speed of the body relative to the ground as Vb and speed of plane relative to the ground as Vp.
From momentum ,VbcosΘ=-Vp .From the non slipping condition ,ωR-Vb=VpcosΘ.This relation seems to be wrong ,the correct aswer is (Vp+VbcosΘ)/cosΘ=ωR which I am incapable of explaining.I also included my work in the pictures

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2. Aug 5, 2017

TSny

Shouldn't the masses show up in the momentum equation? Also, VbcosΘ is not the horizontal component of the velocity of the ball relative to the ground since Vb does not make an angle Θ to the horizontal. The velocity of the ball relative to the ground is not in the same direction as the velocity of the ball relative to the incline. You will need to think carefully about relative velocities in this problem.

I don't think either of these two equations is correct.

3. Aug 5, 2017

haruspex

As TSny wrote, that is incorrect, if Vp is as you have defined it. But it does contain some useful pointers.
In the context of the question, what physical entity does ωR represent?