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-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of John Denker
Sent: Tuesday, September 07, 2010 6:47 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] bound vectors ... or not
On 09/07/2010 02:47 PM, Edmiston, Mike wrote:
www.bluffton.edu/~edmistonm/ConstantTorque.pdf
Very nice.
these are actual devices that have utility in theengineering of real
products.
Another place where the same line (so to speak) of reasoning
shows up is in aerodynamics. Replace the linear force
actuator by an engine+propeller.
Consider the top drawing as a front-engine design and
consider the bottom drawing as a rear-engine design. The
pitching moment will be the same in either case.
Being able to glance at situations like this and appreciate
the invariances is a valuable skill.
==========
There are about ten good ways to think about this.
One way that appeals to me is to represent the torque as a
bivector. The magnitude of the torque is the area of a
parallelogram, which is invariant with respect to shearing
the parallelogram. YMMV, but for me this is very visual and
very intuitive.
It's way better than cross products.
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