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Re: rolling

Skip wrote:

Speaking of rolling.
Some students and I were working on the problem wherein a rope is wou=
nd around a barrel to pull it forward. The rope pulls the top of the =
barrel as it unwinds. When you calculate the acceleration of the barr=
el, it is greater than would it would be if the rope simply pulled at=
the center of mass. This must imply that the friction force on the b=
arrel pushes it forward, a surprising result to us at least.
Anything wrong with our analysis?

Nothing wrong. See:
and references therein. It comes about because you simultaneously
have to consider forces and torques, because linear acceleration =
radius * angular acceleration for no slipping. Thus we do *not* in
general have the condition that the friction is directly proportional
to normal force and other "common" rules about friction.

This particular example is a favorite counter-example of mine to the
question: Is friction always opposite to the direction of an applied
force (in the absence of horizontal forces other than friction and
the applied force)?

This problem is also a wonderful case study in the careful
distinction between pseudowork and real work. See Chabay & Sherwood's
text. Carl
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040