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[Phys-L] spinning skater



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