Rotational Motion of a disk and a box

[mit_hacker]

Homework Statement

A disk and a box of equal mass are released from the top of two inclines both of which are a height h above the ground and make an angle θ to the horizontal. Let the radius of the disk be R. How much sooner does the box reach the bottom of the incline than the disk?
Express your answer in terms of some or all of the variables m, h, theta, and R, as well as the acceleration due to gravity g.

Homework Equations

The Attempt at a Solution

I am completely stumped. Please advice me on how to do this problem.

Thanks a ton for the help and advice!

 

[Doc Al]

Is there friction? My guess is that they want you to assume friction for the disk (so it will roll) and no friction for the box.

Find the linear acceleration of each as they go down the incline. (Apply Newton's 2nd law to both. Be sure to include rotation for the disk.)

 

[mit_hacker]

Thats the problem!

That's precisely the problem. We are asked to assume that there is no friction which is why I am confused as to what will cause the torque on the disk! Please advise.

 

[Doc Al]

If there's no friction, the disk will slide not roll.

 

[mit_hacker]

Thanks for that. I'll keep that in mind and look into the problem again!

 

[Doc Al]

Despite the sloppy wording about "no friction", what I presume they want you to compare is the rolling of the disk versus the sliding of the box. The disk must have friction to roll, but the box should have none. I would solve the problem using that assumption.