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Re: Torque, moment, and couple



Re: r x F = dL/dt; where L = Sum (m*rxv) :

If r is measured from a point fixed in an inertial frame, but v is
measured from some arbitrarily moving origin A, then one can still use the
rotational form of N2 ( rxF= dL/dt ) if the velocity of the origin A is
parallel to the velocity of the CM of the particle system under
consideration (both V_A and V_cm are measured in an inertial frame).

This theorem is often confused with the alternate requirement that the
origin A accelerate toward, or away from, the system CM. This applies
when both r and v are measured from the (non-inertial) origin A).

Texts typically treat one OR the other of these theorems, without
explicitly denoting the different r/v origins involved. Hence the
confusion in the mind of the literate student who reads alternate texts.

Books like Becker and Symon give examples of the usefulness of one or the
other of these theorems. There is also a series of AJP articles on the
use and abuse of these theorems. If requested, I will dig out the refs.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "Leigh Palmer" <palmer@SFU.CA>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, April 09, 2000 1:06 AM
Subject: Re: Torque, moment, and couple


Bob writes:

I once submitted an article to AJP detailing a unified treatment of ang
mom
which explicitly carries two appropriate subscripts. The article was
rejected as adding unneeded complications.

It seems to me that angular momentum of a particle only makes sense
when velocities are reckoned with respect to the frame in which the
reference point for the angular momentum is stationary. How would
one use the quantity r x (m * v) in any frame other then the one in
which v = dp/dt?
. . .
Leigh