# Cylinder rolling down an inclined plane

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...

Thanks!

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.

Last edited:
Thanks. But i know these already.

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

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

Sorry I'm so amateur-ish