Re: A Physics Lesson for the Contributors to this NG

Henri Wilson wrote:
Since few contributors here appear to have any knowledge of basic physics, it
would be remiss of me if I didn't educate them on the very simple topic of
centrifugal force.

Consider a pair of masses connected by a spring and which are rotating at a
constant angular speed in remote space.

m----------------r-----------------------B---R---M

The point B is known as the barycentre. Its position is such that the moments
around it are equal, ie., mr = MR.

Both the objects, m and M, rotate around the barycentre, no matter what their
relative sizes. Even a small orbiting satellite will cause the Earth's C of G
to rotate around their common barycentre.

(No single object can ever rotate in circular fashion without a second one
doing the same, 180 degrees out of phase. In the case of a balanced flywheel,
each unit mass will be opposed by an equal and opposite one. If it isn't
balanced, the whole Earth will shake slightly when it spins)

At constant angular velocity, the spring will be extended at a constant length.
That means it is under tension.

Assuming no lateral movement, a spring will extend when two equal and opposite
forces 'pull' its ends away from each other...in this case AWAY FROM the
barycentre, . The source of those forces is the constant directional change in
the angular momentum vector of the two masses. Because they are confined BY
THE SPRING to moving in a circle rather than tangentially as they would
otherwise do, each mass exerts a continuous OUTWARD force on one end of the
spring.

The values of hte forces are mw^2r and Mw^2R, which are equal. (note: a
positive value indicates 'away from the barycentre')

The spring tension is also -mw^2r (or -Mw^2R). It is negative because it acts
INWARD, ie., CENTRIPETAL.

Concurrently, the two masses are forced to constantly accelerate towards the
barycentre because of the INWARD radial force exerted on them by the spring
tension.

That results in their circular movement around the barycentre at a common
angular velocity 'w'....and mwr = MwR.

The 'inward' acceleration is on m is -w^2r and on M, -w^2R.
The inward CENTRIPETAL forces on the two mases are -mw^2r and -Mw^2R.

<< NO OUTWARD FORCE IS EXERTED
ON THE MASSES THEMSELVES.>>

<< Already Newton recognized that the law of inertia
is unsatisfactory in a context so far unmentioned in this
exposition, namely that it gives no real cause for the
special physical position of the states of motion of the inertial
frames relative to all other states of motion. It makes the
observable material bodies responsible for the gravitational
behaviour of a material point, yet indicates no material
cause for the inertial behaviour of the material
point but devises the cause for it (absolute space or
inertial ether). This is not logically inadmissible although
it is unsatisfactory. For this reason E. Mach demanded
a modification of the law of inertia in the sense that the
inertia should be interpreted as an acceleration resistance
of the bodies against one another and not against "space".
This interpretation governs the expectation
that accelerated bodies have concordant accelerating
action in the same sense on other bodies (acceleration
induction). This interpretation is even more plausible according
to general relativity which eliminates the distinction between
inertial and gravitational effects.

It amounts to stipulating that, apart from the arbitrariness
governed by the free choice of coordinates, the gm v -field
shall be completely determined by the matter. Mach's
stipulation is favoured in general relativity by the circumstance
that acceleration induction in accordance with the gravitational field
equations really exists, although of such slight intensity that
direct detection by mechanical experiments is
out of the question. >>
http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.html


http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRBMDO000070000021212502000001&idtype=cvips&gifs=yes
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html




The centripetal force acts at the point where the spring is attached to the
rotating objects. At constant speed, the spring tension balances the two
centrifugal forces and so the spring remains constantly extended.

What is generally not understood is that the OUTWARD - or centrifugal - force
exerted by one mass on the end of the spring is precisely the INWARD - or
centripetal - force exerted by the other end of the spring on the other mass.
It is exerted through the spring itself, which is effectively 'rigid'.

As is often the case, confusion arises when the rotating frame is considered.
An observer rotating with the above objects will see just a spring that is
extended for no apparent reason. If the spring is cut, he will see the objects
fly of in a curved path and with an apparent acceleration. Both phenomena
(which are different) have been explained by the existence of invisible - or
virtual - outward forces.

These have been correctly termed 'fictitious centrifugal' forces. Note: the
'invisible' forces that keep the spring under tension are not the same as those
which cause the masses to 'magically' move outwards because the former act in a
straight line whereas the latter casue lateral as well as outward movements)

The confusion is one of definition. Many wrongly assume that the existence of a
fictitious 'outward force' in the rotating frame automatically eliminates the
existence of a REAL outward force in the inertial frame.

There is a REAL 'centrifugal' force in the inertial frame. Any old (ie, not
written by a relativist indoctrinee) physics or mechanics text will tell you
all about it.

" Mach's stipulation is favoured in general relativity
by the circumstance that acceleration induction in
accordance with the gravitational field equations really exists"
--A. .Einstein [a relativist? ]


-------
Sue...














HW.
www.users.bigpond.com/hewn/index.htm

Thank christ there is one genuine physicist on the NG.

.

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