Loop the loop. Rotational problem

[makeAwish]

Homework Statement

In this problem you will consider the motion of a cylinder of radius Rcyl that is rolled from a certain height h so that it "loops the loop," that is, rolls around the track with a loop of radius Rloop shown in the figure without losing contact with the track.

Unless otherwise stated, assume that friction is sufficient that the cylinder rolls without slipping. The radius Rcyl of the cylinder is much smaller than the radius Rloop of the loop.

a) Compared to an object that does not roll, but instead slides without friction, should a rolling object be released from the same,a greater, or a lesser height in order just barely to complete the loop the loop?

b) Find the minimum height h that will allow a solid cylinder of mass m and radius Rcyl to loop the loop of radius Rloop.
Express h in terms of the radius Rloop of the loop.

Homework Equations

For part 1, the height is it greater becos the rolling object needs more potential energy to be converted to its translational and rotational kinetic energy and some to overcome friction, while the non rolling object only need potential energy to be converted to translational and rotational kinetic energy?

Both will have translational and rotational kinetic energy, am i right??

For part 2, I'm thinking of using conservation of energy. But for the rotational kinetic energy Kr = 1/2*I*w^2

The omega (w) = v/R

But i duno if R is radius of loop or radius of cylinder..


Pls help me.. Thanks!

 

[rl.bhat]

Radius of cylinder

 

[makeAwish]

Radius of cylinder

hmm. but why? cos i tot r is actually the radius of the circle of rotation which is the radius of loop..

 

[rl.bhat]

Because when the cylinder rolls up the circular loop, it has rotational kinetic energy, translational KE and potential energy. Now apply the law of conservation of energy.
you can apply it at the bottom of the loop and at the top of the loop.

 

[makeAwish]

Because when the cylinder rolls up the circular loop, it has rotational kinetic energy, translational KE and potential energy. Now apply the law of conservation of energy.
you can apply it at the bottom of the loop and at the top of the loop.

hmm i noe tat it has rotational kinetic energy, translational KE and potential energy.. but i still don't understand why r is not radius of loop, for v = r*w.. =x

 

[rl.bhat]

Rotational KE is calculated when the body is rotating about an axis passing through it. And the axis of the loop is not passing through the cylinder.

 

[makeAwish]

Rotational KE is calculated when the body is rotating about an axis passing through it. And the axis of the loop is not passing through the cylinder.

hmm.. i think i get it.. :) thanks! :)

 

[makeAwish]

hmm. how abt part one? is my thinking correct?