Solving a Rotation Problem: Finding Maximum Velocity for a Cylinder

[iitjee10]

Homework Statement

A uniform solid cylinder of radius R=15 cm rolls over a horizontal plane passing into an inclined plane forming an angle $$\alpha$$=30^o with the horizontal. Find the maximum value of the velocity v_o which still permits the cylinder to roll onto the inclined plane section without a jump. the sliding is assumed to be absent.

Homework Equations

The Attempt at a Solution

How do I even go about doing it??

 

[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?

 

[iitjee10]

is there no one to help??

 

[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.

 

[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!

 

[iitjee10]

it goes horizontal . The scan went wrong.