Re: TORQUE

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

> I have a question from a student that I am having difficulty answering
> properly.
>
> We are discussing a pully with a string going over it and the string not
> slipping
> against the pulley with two different masses attached to each end of the
> string,
> one on each side of the pulley.
>
> I drew the free body diagram of the pulley showing a supporting force at the
> center and a Tension downward on the left and also one downward on the
> right of
> the pulley.
>
> The student's comment was "aren't all parts of the string that are in
> contact with
> the pulley also supplying a torque on the pulley?" In other words, he is not
> comfortable with the notion of just the two tensions supplying torque but
> feels
> there are other torques that need to be included in the net torque acting
> on the
> pulley.
>
> What might be a good response to this concern?
>
> Thanks for the help,  David Abineri     dabineri@choice.net

The simple answer is, I think, that the force that the part of the string
that is touching the pulley exerts on the pulley is perpendicular to the
pulley's groove, and thus directed radially. Since the force passes through
the center of the pulley, it exerts no torque that will cause the pulley to
rotate. But that oversimplifies what actually happens when the pulley is
accelerated by different tensions pulling from either side (i.e., the
pulley has inertia). In this context, I think the student's comment may be
correct, but each piece of the string in contact with the pulley is
exerting only a tiny force, in fact one proportional to its length (that is
the length of the piece--element, really--of string). The sum of all the
elements of force exerted by all the elemnts of string then add up to the
force difference between the two tensions. Imagine increasing the length of
string in contact with the pulley, by wrapping it all the way around the
pulley, then the force difference that can be accomodated by the pulley
without the string slipping is larger than what can be handled if only the
minimum necessary string is in contact with the pulley.

Hugh



Hugh Haskell
<mailto://hhaskell@mindspring.com>

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