[quote author=Fu-Kwun Hwang link=topic=1025.msg3758#msg3758 date=1236564946]
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=([color=red]1[/color]/3)m*g*sin? for cylinder or f=([color=red]2/[/color]7)m*g*sin? for sphere.
[/quote]

1. m*g*sin?-f=m*a
2. R*f=I*? imply R*f = (1/2*m*R^2)*(a/R) imply 2*f/m = a

sub back

m*g*sin? - f  = m*(2f/m) imply 1/3*m*g*sin? = f for cylinder ;D