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



You either redefined what is meant by theta or you interchanged <<finite>> with <<more than a million times larger>> but I get your drift--I like the idea of using the principle of virtual work here and taking things to extremes. Very nice.

-----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 9:08 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] bound vectors ... or not

On 09/07/2010 05:19 PM, Jeffrey Schnick wrote:

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 ...

Another way is by the principle of virtual work.

The work done by the linear motor is F * dx.
The work done by the disk is torque * dθ.

As θ goes from 0.00001 to 45 degrees, the work done by the
linear motor is finite.

As θ goes from 45 to 89.99999 degrees, the work is more than
a million times larger.

Same Δθ with different work means different torque.

============

A pin in a slot at point X is not the same as a plain old
force attached to point X. There are leverage issues.

As for the problem of converting uniform rotary motion to
uniform linear motion, a _screw_ is a famously good solution.
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