Re: Banked road

[Herb Schulz <herbs@INTERACCESS.COM>]

Howdy,

> I think it is not only a matter of language; suggest another
> name and I will probably have no objection (unless the word
> is already used to describe something else).
>
> Let us refer to a cylindrical pipe whose inner surface is used
> as a road for a car of mass m traveling along a circle r with a
> constant speed, v. Suppose the cylinder is located far away from
> all stars and that its mass is M. I am at rest in a frame of
> reference which Newton would call "the frame of fixed stars."

Ok. A non-accelerated reference frame.


> To simplify assume tham M>>m so that the pipe is at rest in
> my frame of reference. I see only one force acting of the
> car; it is the CENTRIPETAL force toward the center Fc=m*v^2/r.
> It is the normal force, N, with which the pipe acts on the car.

m*v^2/r is the "ma side" of F(net, on)=ma, it is NOT a force although
it has units of a force.  I've seen too many students who have been
taught to call it the Centripital Force then have both the Normal
Force and the Centripital Force on the F(net, on) side of the
equation.  The only force the pipe is applying on the object is the
Normal Force (neglecting friction).  The reaction to that Normal
Force is a force of the same magnitude and opposite direction as the
Normal Force applied by the object on the pipe.

> The car acts on the pipe and the pipe reacts with an equal and
> opposite force. If the reaction is real (not fictitious) then
> the action is also real in my frame of reference. We need a
> name for the force with which the car acts on the cylinder.
> What is wrong with CENTRIFUGAL?
> Ludwik Kowalski

Then the "Centrifugal Force" is acting on the stationary pipe, not
the object?  I think we need a free body diagram to have anything
make sense here.  That is NOT the way people use the Centrifugal
Force; it is always in the (accelerating) rest from of the rotating
object.

Also, isn't the Coriolis Force term (prop. to dr/dt) and the
d^2r/dt^2 terms should be zero for the rotating object in its own
rest frame.

Good Luck,
--
Herb Schulz
(herbs@interaccess.com)