The condition for rolling without slipping is

v=R*ω (angular velocity) or a=R*α (angular acceleration)

where R is the radius of the ball or cylinder.

Assume the friction force is f

1. m*g*sinθ-f=m*a

2. R*f=I*α

3. I=(1/2)m*R

^{2}for cylinder, (2/5)m*R

^{2}for sphere

solve the above equation will give you

f=(1/3)m*g*sinθ for cylinder or f=(2/7)m*g*sinθ for sphere.

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