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John
1) It's not true. Consider a device with a "front wheel" and a "back
wheel". Starting from rest, I spin up the wheels,
counter-rotating. The
net torque around the CM is zero. The motion of the CM is zero. The
conjectured expression above is zero squared. Yet the kinetic energy
increases.
I think this is the best gedanken device yet that illustrates the point
D is making. Any comments from others regarding this example?
Joel R.