Finding the angle where acceleration is 0 in the system....

[Vitani11]

Homework Statement

A small solid cylinder with mass m and radius r is attached to a larger cylinder with mass M and radius R resting on a horizontal surface. Jennifer wraps a string around the small cylinder and then applies a light tension to the string. If she holds the string vertically, the cylinder will roll left; if she holds the string horizontally to the right, the cylinder rolls to the right. What is the angle between the string and the horizontal so that the cylinder remains stationary when a light tension is applied to the string? The coefficient of static friction between the larger cylinder and the surface is (mu)s and for kinetic friction it is (mu)k.

Homework Equations

I = 1/2*MR^2 moment of inertia
T is tension
Torque= I alpha = radius * T

The Attempt at a Solution

 

[Vitani11]

Here is a picture with prompt

 

[Vitani11]

Trying to do this now. Will upload my attempt soon.

 

[Vitani11]

...

 

[haruspex]

...

The image of your attempt is too hard to read. Please take the trouble to type your working into the post. Images are really for diagrams and textbook extracts.
Think about the different situations the question poses. With the string vertical, the cylinders have a tendency to rotate one way; with it horizontal, the tendency is to rotate the other way. You are looking for an angle where there is no tendency to rotate.
If there is no tendency to rotate about the mass centre, is there a tendency for the point of contact to move left or right? What does that tell you about the frictional force?

What physical entity leads to rotation?

 

[Vitani11]

I solved this earlier today but thank you.