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



Hi all-
I think that there may be a semantic confusion here - namely a
pun on the phrase "centripetal force." Michael writes, in part, that
he has a handout that sez:
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If the object is following a curved path, there must be a component of
the net force pointing perpendicularly to the velocity vector. This
component is often called the centripetal force. However, the
"centripetal force" is not a force in itself, it is a component of the
other forces that you have already drawn on your free-body diagram.
Therefore, do not draw a centripetal force vector on your free-body
diagram. The trick is to make sure that you get the acceleration
correct. For curved paths you must realize there is an acceleration
component in the direction perpendicular to the velocity. The
magnitude of this acceleration is v^2/r. If you include that
acceleration when you set F(net) = ma, then everything should work out
correctly even though there isn't any force labeled "centripetal force"
anywhere in your drawings. Align one axis of your coordinate system
with the velocity, suppose this is x. Align one of the other axes with
the instantaneous center of curvature of the path, suppose this is y.
a(y) = v^2/r, and F(y)(net) must equal ma(y).
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For simplicity consider a free-body diagram of an electron
moving transversely to a uniform magnetic field. There is a single
force acting on the electron, perpendicular to the direction of motion.
I can label this force VxB (caps are vectors), or I can label it "centripetal
force" F_c because it is the force that makes the trajectory curve. I must
recognize, of course, that
F_c = VxB.
The confusion arises if one does not make the above connection, in which
case the student may think that there is an F_c other than VxB.
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