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Homework Statement
A solid cylinder rolls down an inclined plane because of stiction. How does angular velocity change over time?
Given:
##m,R,g,\alpha,\mu## where ##\mu## is the friction coefficient
Homework Equations
[/B]
##J_{cm} = 1/2 m*r^2## moment of inertia
m = mass of the cylinder
Parallel Axis theorem: ##J=J_{cm}+mr^2##
## M = I*d\omega/dt ## = Torque
The Attempt at a Solution
First I thought I take the torque at the center of mass pulling it down
##R*mg*sin(\alpha)=d\omega/dt*(J_{cm}+mr^2)##
which gives me as an end result:
## d\omega/dt = \frac{2*g*sin(\alpha)}{3*r} ##
= ## \omega = \frac{2*g*sin(\alpha)}{3*r}*t ##
Then I thought it would have been simpler if I looked at the point of friction:
## M/J = r \times F / J = r*F_{friction}/J = \mu*r*mg*cos(\alpha)/J=d\omega/dt ##
=## \frac{2*\mu*g*cos(\alpha)}{3r}=d\omega/dt ##
=## \frac{2*\mu*g*cos(\alpha)}{3r}*t=\omega ##
Are both correct, one of them or both garbage?
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