Re: Rolling friction (again)

["John S. Denker" <jsd@MONMOUTH.COM>]

Bob Sciamanda wrote:

> John,
> I want to commend you on a very nice summary at the URL:
> http://www.monmouth.com/~jsd/physics/car-go.htm#sec-friction.

:-)

> However, I would like to try (again) to disabuse you of your
> mis-appreciation of the Work/KE theorem,

You're welcome to try.

> By the Work/KE theorem I here mean (and I think you also mean) the
> statement that the line integral of the net external force on a system
> evaluated over the trajectory of the Center of Mass of that system is
> numerically equal to the change in the kinetic energy of that system
> (evaluated at the trajectory end-points).

This is simply not true, assuming the ordinary
definition of kinetic energy.

Counterexample:  Two coaxial flywheels plus a spring.
Initial KE=0.  Spring sets flywheels spinning in
opposite directions.  Final KE>0.  Net external force
on the system is zero throughout.  Motion of CM is
zero throughout.  Line integral is zero squared.

> This is simply a numerical
> equality and is easily proven to apply to any system of enumerated
> particles/objects.

It's bad luck to prove things that aren't true.

Also, I recommend and request avoiding the term
particles/objects.  What's true for particles isn't
necessarily true for complex objects.

========

For a clearer picture of what I believe and don't
believe, check out
  http://www.monmouth.com/~jsd/physics/momentum-squared.htm

I've added cross-references to this in the car-go
document in hopes of reducing confusion......