Date: Dec 21, 2012 2:28 PM
Author: Peter Duveen
Subject: Re: Physics problem --ball rolling down an inclined plane
Bob, the "goal" is for students to solve what should be a very simple problem in dynamics, but which turns out to be beyond the ability of Newton's formulation to solve.
The point being that, usually, if we are discussing an inclined plane, and doing various experiments, the acceleration is quite a bit impeded if one is using a rolling object.
Not very powerful physics if one cannot solve the seemingly simple problem of a ball rolling down an inclined plane.
Louis, to make the problem simpler, I believe it is best to deal with a hollow cylinder, so there's no complicated integration over a solid object with varying dimensions, such as a sphere. It becomes much simpler mathematically. If my memory serves me correctly, the hollow cylinder rolls down the plane with half the acceleration of a body sliding down the inclined plane without friction.
As far as using energy, one must then introduce the principle of conservation of energy. D'Alembert's principle basically says that the resultant accelerations multiplied into the masses, when reversed, are a system of forces in equilibrium with the applied forces. My preference would be to introduce D'Alembert's Principle.