On Dec 21, 2012, at 2:28 PM, Peter Duveen <pduveen@yahoo.com> wrote:

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.

Solving problems isn't the goal of teaching physics. If that was the goal then just give them formulas. The goal of teaching physics is to teach the careful and quantitative analysis of a physical situation based on underlying principles. It is theorizing about the unobservable in order to explain the observable.

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.

I think Lou's suggestion is more relevant and stays truer to my definition of teaching physics. First, it relies on a fundamental and simple principle, the conservation of energy. Secondly, the rotational equations nicely mimic at least the translational versions that the students are already familiar with and should have derived. I would prefer that the students at least be presented with the derivation of rotational versions before they are let loose with the engineer's book of mathematical formulae. But none the less, there is easily enough here to do a careful quantitative analysis of the situation that the students can follow and grow from.

D'Alembert's principle on the other hand is a mathematical conclusion (like Maxwell's equations) far too large for any of the students to understand. You lose both the element of starting with fundamental principles (that the student can at least begin to understand) and the element of careful analysis.

Not very powerful physics if one cannot solve the seemingly simple problem of a ball rolling down an inclined plane.

In conclusion, that isn't the point.:)

Bob Hansen