# A cylinder rolls without slipping- find the angle

1. Nov 7, 2009

### vballgurl154

1. The problem statement, all variables and given/known data

A cylinder with radius R and mass M rolls without slipping down an incline plane with angle$$\theta$$. The coeff. of friction is $$\mu$$. Find the maximum value for the angle for the cylinder to roll without slipping.

2. Relevant equations

The moment of inertia for a cylinder is I=(MR^2)/2.
w=v/r

3. The attempt at a solution

If the cylinder rolls without slipping, energy must be conserved. So Mgh=1/2Mv^2+1/2Iw^2. If you plug in the equations from above and divide all terms by M, gh=3/4v^2.
So we need to find v.
The equation for the x-component of force (where x is along the plane of the incline), F=mg(cos$$\theta$$-$$\mu$$)=ma
and the y-component
F=0=N-mgsin$$\theta$$ or N=mgsin$$\theta$$

I have no idea where to go from here and I'm not quite sure I did all of this right. Thank you so much for any help!!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 7, 2009

### Tzim

You should think when you will have the minimum value of angle.When you have the maximum of static friction.Also i think you have a mistake.In the direction of the slope the forces are Wy=mgsinθ and T<=μN

3. Nov 7, 2009

### Tzim

Also N=mgcosθ not mgsinθ