Suppose a particle of mass

*a * = *r A *

where *A * is the angular acceleration (i.e. the rate at which the
angular velocity of the rod is changing) and *a * is the
instantaneous linear acceleration the particle experiences out on the
circle.

By Newton's second law for linear motion, if we apply a force *F *
to the particle, then *F * = *m a *. On the other hand, since
we have a rotating system, we
would like to work with *torque *, instead of force, so we
multiply both sides of the equation by *r *. Then

*T * = *F r * = *m r a *.

Finally, we use the equation derived about, to convert from linear acceleration to angular acceleration:

*T * = *m r a * = *m r * (*A r *).

Rearranging terms gives the desired formula *T * = (*m
r *^{2}) *A*.

The Geometry Center Calculus Development Team

Copyright © 1996 by The Geometry Center. Last modified: Fri Apr 12 15:52:12 1996