Rotational motion of a ball

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These problems have diagrams with them so I posted those pictures are at
http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=21023924&imageID=1420239256

1) A spherical ball rolls up an incline. Determine the acceleration of the ball and the magnitude and direction of the friction force.

Based on the diagram, I know that friction is pushing the ball up the incline. I know that the ball is sphere so I = 2/5 MR^2. I drew free body diagrams with N pointing diagonally up to the left, mg pointing straight down, and friction point diagonally right and along the incline.

so

y: mgcos(theta) - N = 0
x : mu*mg*cos(theta) - mgsin(theta) = ma

a = mu*g*cos(theta) - gsin(theta)

I don't know mu and friction so I cannot solve for a. What am I missing to allow me to solve this problem? The correct answers are a = (5/7)g*sin(theta) and f = (2/7) mg *sin(theta). I don't know what I am missing.

2)

A string unwinds from a disk and the disk rolls smoothly. Explain why the direction of friction is unknown in the problem. The picture for this is at the link above.

I don't know why. Is it because of the fact that the disk will be pulled to the right, and it is uncertain whether it would roll. If it rolls to the right, wouldn't friction resist to the left. But then again, there must be friction pushing it to the right to make it roll. Why don't we know the direction of the friction. Am I on the right track explaining it?

Thanks for your help.
 

Answers and Replies

  • #2
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For the second question, in physics world once a wheel is moving with no acceleration (forget how it got moving), there is no net force acting on it. You might think in order for the wheel to move there has to be friction, but think of a wheel that began to spin on a road and then hit a patch of ice. It would continue to spin because no friction acts on it
 
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Thanks very much.
 

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