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I have an issue with the way that Newton's Second Law is presented in many
texts and webpages when rotation is involved.
e.g. http://en.wikipedia.org/wiki/Angular_acceleration
An analogy is made between F=ma and T=IA (I'll use I for moment of Inertia
and A for Angular acceleration so I don't have to keep writing alpha).
Elsewhere, the analogy is made between F=dp/dt and T=dL/dt (L being angular
momentum with L=Iw and w being angular velocity).
For most of introductory level physics, one doesn't get into much trouble
using the two forms F=ma and F=dp/dt interchangeably because an object
can't change its mass at will if mass does not pass in and out of its
boundaries.
However, the two forms T=IA and T=dL/dt can give very different results
because a rotating object can easily change its moment of inertia even if
there is no interaction with the external world. For a spinning skater,
T=IA would predict that with no external torque acting that A must be
constant - regardless of changes in moment of inertia. But T=dL/dt predicts
that the rotation will speed up if the skater's arms are pulled in.
I only bring this up because so many texts and webpages don't emphasize
how T=IA assumes that the object is rigid.
As you can probably guess - I'm grading final exams :-)
Bob at PC
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