Re: Atwood's machine problem

[John Denker <jsd@AV8N.COM>]

Dan Crowe wrote:
> An alternate perspective is to use the lever arm (moment arm) formalism.
> The lever arm is the perpendicular distance from the origin to the line
> of action of the force.  In this case, the lever arm equals the radius,
> R, of the pulley.  The torque, T, equals the lever arm times the force,
> F:
>
> T = RF
>
> which is nonzero.

OK, that works.

It's amusing that R drops out of the result, for any
nonzero R.  Meanwhile, the R=0 limit is pathological.
I suspect that this creates a psychological barrier
that makes this solution harder to find.


Herb Schultz wrote:

> The r vector points from the Pivot Point at the center of the Pulley Wheel
> while the CM of the Monkey hangs from a line which is tangent to the
> Pulley's edge.

That's not wrong as stated, but I don't like it as much, because it
is a compound sentence.  The important part is the edge of the
pulley.  The part about the CM of the monkey is dodgier ... you
can set up multi-pulley systems where the CM argument cannot be
directly applied, while the pulley/edge/tangent argument remains
valid for each pulley separately.

==========

I still like my reflected-force argument, since it applies to
situations such as a rope draped over a frictionless table, where
angular momentum arguments would be nonobvious to say the least.