Cylinder rolling down an inclined plane

[trisectedangl]

This is an even-numbered problem in my textbook that I'm looking at early though it hasn't been taught by my lecturer yet, because I need to know the concepts underlying it for a similar problem. Cld someone help me?

Homework Statement

Consider the case of a hollow cylinder rolling down a plane inclined to the ground at an angle β. There is a small piece of plasticine stuck to a fixed position on the cylinder's inner circumference. What is the acceleration in this case?

Assume the small piece of plasticine to be a rigid cylinder of radius r and mass m, and the hollow cylinder to be of radius R and mass M.

Homework Equations

The formula for acceleration of hollow and filled cylinders

The Attempt at a Solution

Can't solve...


Help please?


Thanks!

 

[shoeman]

i'm not too sure but I'm throwing it out there.

(whenever i type "I" it's for moment of inertia, when talking about myself i'll use lower case i).
i assume you need first to find the moment of inertia through the center of the body, then use Steiner's equation to find I on the edge that is touching the incline.
The hardest part here is that I of the edge that is touching the incline changes according the where the plasticine is, so you would have to find I as a function of θ (angular position of the plasticine).
and θ is a function of how the body rolls.
if it's rolling without slipping you can do a moment equation on the edge of the body
Ʃτ=Iα
α=a/R
and maybe throw in a force equation or two, i think you should reach a good equation with θ and it's derivatives...
hope this helped.

 

[trisectedangl]

Thanks. But i know these already.

By the way, there is friction, which has nonzero torque on the centre of the can.

 

[trisectedangl]

Could you be more specific and show how you did the maths?

Sorry I'm so amateur-ish