A ball or cylinder rolling (without slipping) down in a down hill slope.
The condition for rolling without slipping is
v=R*? (angular velocity) or a=R*? (angular acceleration)
where R is the radius of the ball or cylinder.

Assume the friction force is f
1. m*g*sin?-f=m*a
2. R*f=I*?
3. I=(1/2)m*R[sup]2[/sup] for cylinder, (2/5)m*R[sup]2[/sup] for sphere
solve the above equation will give you
f=(1/3)m*g*sin? for cylinder or f=(2/7)m*g*sin? for sphere.



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