(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A solid cylinder of radius R sits at the top of a slope of angle theta. When it rolls down, what is the minimum coefficient of friction (k) required to make the cylinder roll without slipping?

2. Relevant equations

Fx: mgsin(theta) - kmgcos(theta) = ma

Torque: kmgRcos(theta) = mR^2 * Alpha

3. The attempt at a solution

In order for the cylinder to roll without slipping, the tangential acceleration at the edge must be twice the acceleration of the center of mass (right?). Therefore, we solve for where Alpha = 2a/R.

From Torque:

kmgRcos(theta) = mR^2 * 2a/R

kgcos(theta) = 2a

Substituting for a from Fx:

kgcos(theta) = 2gsin(theta) - 2kgcos(theta)

k = (2/3)tan(theta)

The book's answer is (1/2)tan(theta).

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# Homework Help: Rolling a cylinder down a slope.

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