Re: origin of inertia

From: JM Albuquerque (jm.aREM.OVE_at_sapo.pt)
Date: 03/26/05 

Date: Sat, 26 Mar 2005 05:19:36 -0000

"bz" <bz+sp@ch100-5.chem.lsu.edu> escreveu na mensagem
news:Xns9624C46BBE338WQAHBGMXSZHVspammote@130.39.198.139...
> "JM Albuquerque" <jm.aREM.OVE@sapo.pt> wrote in news:3ajamkF6ci6jnU1
> @individual.net:
>
> >
> > "bz" <bz+sp@ch100-5.chem.lsu.edu> escreveu na mensagem
> > news:Xns9624684D75F8DWQAHBGMXSZHVspammote@130.39.198.139...
> >> "JM Albuquerque" <jm.aREM.OVE@sapo.pt> wrote in news:3ags89F6bcq1pU1
> >> @individual.net:
> >>
> >> > In the gyroscopic effect there is no acceleration.
> >> >
> >> > Euler's equations predict that one can turn a
> >> > spinning sphere without notice any force.
> >> >
> >> > I've been around with those ideas and looking
> >> > for gyroscopic spheres.
> >> >
> >>
> >> Gyroscopes work because angular momentum is conserved.
> >
> >
> > It depends on what you have in mind for "work".
> >
> > A gyroscope free from any constrain, whose mass is
> > balanced with gravity, will keep pointing the same
> > direction relative to the distant stars and angular
> > momentum is conserved.
> >
> > But when a gyroscope is precessing due to an
> > unbalance caused by gravity (a torque due to gravity)
> > angular momentum is not conserved.
>
> Angular momentum is conserved. It is a vector and it points in the
> direction of the axis of spin.

The angular momentum vector that points in the
direction of the axis of spin is conserved all right.
But it is only conserved in its amplitude, not in
direction as long as precession occurs.

You should read carefully the previous posts.

> The physics of a spinning top are well known. When a torque is applied
> perpendicular to the axis of spin of a gyroscope or a top, conservation of
> angular momentum causes a resultant torque perpendicular to the applied
> torque and the angular momentum vector.

It's not so.
There is no conservation of the total angular momentum
once a torque is applied. A torque is a force and a force
requires acceleration (from Newton's Law).
Where is the acceleration ?
What do you see accelerating ?

In the gyroscopic effect nothing accelerates.
There is only the constant angular frequency of the main
spinning wheel (whose angular momentum is conserved
because there is no acceleration) and the angular
frequency of the precession motion which is also
a constant angular speed.
The mass under gravity causes a torque but the mass
doesn't move vertically, so it produces no work.

>The direction of the resultant
> torque can be predicted by use of the right hand rule.
>
> Since gravity continues to exert a component that is perpendicular to the
> axis of rotation, conservation of angular momentum produces a resultant
> force at rotates so as to always be right angles to the force exerted by
> gravity, the top 'wobbles' or precesses in a circle.

There are no accelerations. Hence no other forces, nor
other torques more then the torque due to gravity (whose
acceleration is "g" and natural even if it doesn't move).
The torque vector T due to gravity is balanced by the
external product of the main angular momentum L
and the precession angular frequency vector wp,
T = L x wp
T = mg.r (dot product)
So that:
wp = (mg.r) / L

Total angular momentum is not conserved.
Only the amplitude of the main angular momentum L vector
that points in the direction of the axis of spin is conserved
but then you have a new angular frequency due to
precession to sum, so that L(total) = L + Lp

> > The total angular momentum increases by the
> > amount of Lp = Ip wp, being "p" precession.
> >
> > Angular momentum is conserved only as long as
> > no external torque is applied.
>
> from Halliday and Resnick, Fundamentals of Physics"
>
> "A classroom demonstration that illustrates the vector nature of the law
> of conservation of angular momentum is worth considering.
> A student stands on a platform that can rotate only about a vertical axis.
> In his hand he holds the axis of a [spinnin] rim-loaded bicycle wheel with
> its axis vertical.... The student tries to change the direction of
> rotation of the wheel. What happens?"
>
> Of course, angular momentum is conserved and the student and platform
> rotate.

That's is only true if the student accelerates the spinning
rim-loaded bicycle.
If the student rotate the spinning rim-loaded bicycle at
constant speed (no acceleration) nothing happens and
the platform doesn't rotate.

Get it ?

The "magic" only works with gravity.
Any other kind of external torque requires an accelerated
motion.
Precession is not an accelerated motion.

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