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I have been thinking about this problem for a while to no avail. Any input would be greatly appreciated. Thanks!

1. The problem statement, all variables and given/known data

A solid sphere of mass M and radius R rolls without slipping down a 30 degree incline (see figure attached).

What is the linear acceleration, a, of the sphere down the incline?

2. Relevant equations

I=(2/5)MR^2

torque = (Ia)/R = rxF

3. The attempt at a solution

I only know of two ways to solve for this: energy methods or torque methods. To do torque, I would need to know the value of the static friction that is keeping the ball from slipping, but I don't have that information. For energy methods, I don't have a height from where the ball began to roll, so I don't see how I can use that.

Here is my attempt at torque:

torque = (-Ia)/R = -fR where f=force of static friction

=> Ia = fR^2 => substitute I=(2/5)MR^2 => (2/5)(MR^2)a = fR^2 => f=(2/5)Ma => a=(5f)/(2M)

I don't know where to go from here. The answer is (5/14)g. I must be missing some type of other alternative to solving this problem, but I can't think of what. Thanks so much! I appreciate it.

Ryan

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# A ball rolling down an incline

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