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

For clarification, what I refer to as the upper diagram in my previous
message is the first of the three diagrams, and what I refer to as the
lower diagram is the second of the three diagrams.

Another way to see that the torque exerted on the disk by the pin in the
first configuration is greater than the torque exerted on the disk by
the pin in the second configuration is to recognize that the leftward
force of the pin on the wall of the slot produces the same torque in
both cases but in the first configuration, the force of the pin on the
wall of the slot has an upward component which makes an even greater
contribution to the total torque making the total torque in the first
configuration more than double that of the first. (There is no upward
component of the force of the pin on the slot in the second
configuration.)

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of Jeffrey Schnick
Sent: Tuesday, September 07, 2010 6:16 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] bound vectors ... or not

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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