On Thu, 20 Dec 2012 14:32:50 -0700, Peter Duveen <email@example.com> wrote:
> High school physics students are taught so-called Newtonian mechanics, > but cannot solve the simple problem of a ball rolling down an inclined > plane. Rigid bodies are outside the purview of Newtonian mechanics, as > Newton himself seems to have admitted in The Principia. However, the > application of D'Alembert's Principle yields a solution to this simple > problem. The problem becomes particularly simple when worked out for a > thin cylinder or ring rolling down an inclined plane. Should high school > students be introduced to D'Alembert's Principle?
Have they been introduced to moments of inertia? That's a topic that's mostly beyond the high school level because one must be able to set up a multi-dimensional integral to compute them.
Even then, I'd think that Conservation of Energy might give an easier solution.
- --Lou Talman Department of Mathematical & Computer Sciences Metropolitan State University of Denver