The kinetic energy referred to in the CM Work/KE theorem being discussed
is (1/2) M V^2, where total M is the mass of the system and V is the speed
of the CM of the total system. In your two flywheels plus spring system
this KE remains zero throughout. (As you obviously realize and have stated
: " Motion of CM is zero throughout.")
I think we have a communication/semantics problem.
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, January 21, 2003 2:38 PM
Subject: Re: Rolling friction (again)
| 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......