Re: TORQUE

[Robert Carlson <Raacc@AOL.COM>]

David,

First, I believe that tension is something internal to the string.  In my
opinion, it is really a frictional force between the surfaces of the string
and the pulley that causes the pulley to rotate.  When there is no slipping,
then it is a static frictional force between these surfaces that causes
angular acceleration.  However, this can be mathematically treated as the
equivalence of two different tensions on each side of the pulley similar to
two separate strings on both sides of a mass in a linear situation.  This can
be  expanded to an infinite number of infinitely small connected masses with
infinitely small differential tensions.  In this sense, your student is
correct in that the tension varies over the pulley.  However, the overall
mathematical equivalent effect is the difference in the two tensions on either
side of the complete system.  You might approach this as a linear problem with
masses connected by strings.  First use one mass with two external string
tensions on both sides, assume a constant acceleration and analyze the free
body diagram.  Then split the mass in two equal parts with connecting strings
and assume the same acceleration.  Split the initial mass in three equal
parts, with connecting strings, and again assume the same acceleration.  In
all cases look at all masses separately and as a combined system with emphasis
on the external tensions when examining your free body diagrams.  You should
be able to convince your student that while the tensions within the system do
vary, the external tensions do not.  Hence, the math reduces to the two
external tensions if you consider the whole mass system.

Bob Carlson

In a message dated 12/10/98 8:58:23 PM Central Standard Time,
dabineri@CHOICE.NET writes:

> 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