What is the minimum coefficient of friction required to maintain pure rolling motion for a disk?

What is the minimum coefficient of friction required to maintain pure rolling motion for a disk down an incline?



So the acceleration of a disk rolling down a slope is a = 2/3 * g * sin(theta) , but how do you find the minimum coefficient of friction needed so that the disk won't slip? Can anyone solve this problem for me in terms of theta and g?What is the minimum coefficient of friction required to maintain pure rolling motion for a disk?Note that if the body had no moment of inertia (all mass at the center), no torque, thus no tangential force, would be needed to accelerate it. The only force needed to provide tangential acceleration to a rolling body is the acceleration times the "effective" mass at the rim meff; for a disk meff = m/2.

So F(tangential) = meff*a = m/2 * 2/3*gsin(theta) = mgsin(theta)/3

Fnormal = mgcos(theta)

Ffric must be (at least) = Ftangential ==%26gt;

mu = Ffric/Fnormal = tan(theta)/3What is the minimum coefficient of friction required to maintain pure rolling motion for a disk?Thank-you. Yes, effective mass is not usually referred to in physics texts, but I find it a useful concept.

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