# Rolling Body mechanics

## Homework Statement

In the picture ,problem 8.29

## Homework Equations

Energy conservation ,velocity relation ,momentum

## 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

#### Attachments

• 15019306742351633013540.jpg
58.9 KB · Views: 362
• 1501931174371366449559.jpg
24.2 KB · Views: 330

TSny
Homework Helper
Gold Member
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 .
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.

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

haruspex
Homework Helper
Gold Member
2020 Award
(Vp+VbcosΘ)/cosΘ=ωR
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?