Minimum Angular Speed to start SLIPPING BEFORE ROLLING WITHOUT SLIPPING

[Ransalu]

Homework Statement

Minimum Angular Speed to start SLIPPING BEFORE ROLLING WITHOUT SLIPPING.

Homework Equations

A cylinder of mass M with radius r is given an angular speed of an w about an axis, parallel to its length , which passes through its centre. The cylinder is gently lowered onto an upward direction of inclined frictional surface which makes an angle alpha with the horizontal axis. The coefficient of friction of the two surfaces is u.
*What is the minimum angular speed w to start slipping before rolling without slipping?
*If the angular speed w is adequate to start slipping how long does it take before the cylinder starts to roll without slipping?

The Attempt at a Solution

I can see no possible way to reach the first part of the question. I can't realize why does the cylinder slip firstly before purely rolling. Is it slipping with rolling or without rolling at the begining?

 

[Delphi51]

Usually you begin this kind of problem by finding the maximum up-the-hill force you can get - which is the friction force minus the component of weight down the hill. Then use F=ma to get the maximum acceleration. Alas, this problem doesn't ask for the max acceleration, but rather the max speed. If the cylinder is not moving tangentially when it contacts the surface, any w without slipping will require infinite acceleration at the moment of first contact with the surface as its speed changes from zero to rw instantly. It can't have that so it will slip.

If we interpret the "touches gently" as a cylinder that is moving in the direction uphill along the ramp just before it touches then no acceleration is required to continue moving up the ramp at that same w or rw. So it won't slip.

Note that the cylinder must use up its rotational energy to climb the hill. As it goes up, it will decelerate. I don't see how this gives us any grip on the problem, either.

Looks like an impossible problem to me, too. I will be most interested in seeing a solution!