Re: [Phys-l] bound vectors ... or not

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

The torque on the disk in the upper diagram is greater than the torque
on the disk on the lower diagram.  In both cases the force exerted by
the pin (vector F_p) on the slot wall is perpendicular to the slot wall.
That force is (very close to being) perpendicular to the position vector
of the point of application of the force relative to the axis of the
disk (vector r).  Hence the magnitude of the torque is just
(approximately) r Fp (the product of the magnitudes of the vectors).
Both r and Fp are greater in the upper diagram since, in the upper
diagram, the point of contact (between the pin and the slot wall) is
farther away from the axis of the disk and the constant horizontal
component of the force represents the smaller component of the total
force (vector F_p) in the upper diagram (expressed as a horizontal
component plus a vertical component) whereas it is the only component of
the force (vector F_p) in the lower diagram.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Edmiston, Mike
> Sent: Tuesday, September 07, 2010 5:47 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] bound vectors ... or not
>
> If you want to see a drawing of a device that utilizes a constant-
> magnitude force acting along a constant line-of-force to rotate a disk
> with constant torque, view the drawing and text at the following
> link...
>
> www.bluffton.edu/~edmistonm/ConstantTorque.pdf
>
> The sliding contact allows a variable point of attachment that allows
> the line-of-action to remain constant.  This shows that any point of
> attachment along the line-of-action yields the same torque.  You do
not
> need to specify the point of attachment.
>
> The disk could be powered by a rotary motor, and the linear motor
would
> then be replaced with a linear bearing.  If the motor has constant
> torque then the rod will be driven with constant force along a
constant
> line-of-action.
>
> Of course there is limited range of action in either of these cases,
> but these are actual devices that have utility in the engineering of
> real products.
>
> To me, this shows a different way of thinking about force vectors,
> point of attachment, and torque from the way I had thought about them
> in the past.
>
>
> Michael D. Edmiston, Ph.D.
> Professor of Chemistry and Physics
> Bluffton University
> Bluffton, OH 45817
> (419)-358-3270
> edmiston@bluffton.edu
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