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Re: Newton's 3rd law? was Re: inertial forces (definition)



The centripetal component of the acceleration is v^2/r .
The centripetal component of the net force is mv^2/r .

As to what is shown in any particular diagram, that is purely a matter of
convention and personal convenience.
One man's fbd may be another man's notes.

Bob

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

----- Original Message -----
From: JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE,
IL 60439 <JLU@HEP.ANL.GOV>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, October 23, 1999 4:09 PM
Subject: Re: Newton's 3rd law? was Re: inertial forces (definition)


Hi Bob Sciamanda-
I think that you misuse the meaning of the equal sign when you
write:
***************************************************
If I know the radius of curvature and the speed of a particle's present
motion (in a Newtonian inertial frame) then I can take advantage of the
fact that the component of the net force (of the universe) on this
particle, perpendicular to its present velocity direction, is mv^2/r and
is directed toward the center of curvature of its present path.
********************************
We use the equal sign in two different ways. One way is to
express
an identity, such as:
VxB = |V||B|sine(theta).
The other is two express the idea that two different
measurements must
give the same numerical result, such as:
F = mA (caps are vectors in these equations.
With this understanding I object to your statement that the
"force"
"is mv^2/r". That quantity is the acceleration, which Newton teaches us
is
numerically equal to the centripetal component of the force.
The difference is important when one uses the fbd to write down
Newton's
law, as applied to the fbd. The fbd shows the forces (the left side of
the 2d law).
The student writes down each force component followed by an equal sign.
What goes
on the right of the equal sign? The accelerations, which are not shown
on the fbd.
If the object is instantaneously moving on a curve with radius r along
an axis, with
speed v perpendicular to that axis, then the acceleration on the right
side of the
appropriate equation is mv^2/r.
Regards,
Jack

"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography