# A rotation problem

1. Dec 11, 2008

### iitjee10

1. The problem statement, all variables and given/known data
A uniform solid cylinder of radius R=15 cm rolls over a horizontal plane passing into an inclined plane forming an angle $$\alpha$$=30o with the horizontal. Find the maximum value of the velocity vo which still permits the cylinder to roll onto the inclined plane section without a jump. the sliding is assumed to be absent.

2. Relevant equations

3. The attempt at a solution
How do I even go about doing it??
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Dec 11, 2008

### rl.bhat

when a uniform solid cylinder rolls over a horizontal plane passing into an inclined plane, its center of mass moves through an arc. In this problem, what is the angle subtended by the arc at the edge of the inclined plane? During this rolling what is the distance through which the center of mass falls? And what is the time taken?

3. Dec 14, 2008

### iitjee10

is there no one to help??

4. Dec 14, 2008

### rl.bhat

When a uniform solid cylinder rolls over a horizontal plane passing into an inclined plane, its center of mass moves through an arc. It experiences a centrifugal force due to circular motion. To keep it on the edge of the inclined plane, a component of weight must act along the radius. So mv^2/R = mg*cos( theta). Now solve for v.

5. Dec 14, 2008

### Dr.D

Your figure shows the cylinder rolling up one plane before it begins to descend the second plane. This conflicts with the statement that it rolls on a horizontal plane before it encounters the descending plane. Just which case it it? It really does matter!

Ask yourself, (1) what would it mean for the cylinder to jump? What would be happening if the cylinder did jump?

(2) After you have decided what the conditions for a jump are, then ask yourself how you will establish them analytically.

This is a good problem. Good Luck!

6. Dec 15, 2008

### iitjee10

it goes horizontal . The scan went wrong.