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Rotational Inertia Question

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Rotational Inertia Question K. M. Kirby, esq. 09-28-2006
Posted by K. M. Kirby, esq. on September 28, 2006, 6:13 pm
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Regarding the current rotation speeds of the Moon and Mercury, is there
any possibility that these two objects had more spin velocity in the
distant past?

This question is related to another, and that is: does a freely
rotating planet lose some of its rate of spin for every geographical
readjustment occuring during true polar wander?


This might make an interesting experiment for the ISS -- Having a
spinning globe, with an extra mass added near the pole, and observing
what happens to spin rate as the mass migrates to the equator of this
globe.

Does friction cause some of the rotational inertia to be lost to heat,
perhaps?


Posted by Henry Spencer on September 30, 2006, 12:58 am
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>Regarding the current rotation speeds of the Moon and Mercury, is there
>any possibility that these two objects had more spin velocity in the
>distant past?

It is essentially certain that they did, but the angular momentum was
gradually transferred to either the parent body or the orbit via tidal
interactions. (Similarly, Earth's rotational angular momentum is
gradually being transferred to the Moon's orbit now, moving the Moon out
and slowing the Earth. Eventually the Earth will end up with one side
always facing the Moon, in the same way that one side of the Moon always
faces the Earth -- see the Pluto-Charon system for an existing example.)

>This question is related to another, and that is: does a freely
>rotating planet lose some of its rate of spin for every geographical
>readjustment occuring during true polar wander?

Even postulating that "true polar wander" actually takes place, no.
Angular momentum doesn't disappear. Moving mass outward from the axis of
rotation slows the spin, *without* changing the angular momentum; if that
mass then somehow gets moved back inward, the spin picks up again. The
only way a planet can actually lose angular momentum is to transfer it to
something else, e.g. as noted above.

>This might make an interesting experiment for the ISS -- Having a
>spinning globe, with an extra mass added near the pole, and observing
>what happens to spin rate as the mass migrates to the equator of this
>globe.

This can be calculated without difficulty; there is no need to experiment.
The physics of such shifts in rotation axis are well understood, not least
as a consequence of experience with the dynamics of spinning satellites.

>Does friction cause some of the rotational inertia to be lost to heat,
>perhaps?

"Rotational inertia" is not a well-defined quantity. The well-defined
quantities involved are angular momentum and rotational kinetic energy,
and it is important to distinguish between the two. Angular momentum, as
noted above, can be transferred but cannot be lost. Rotational kinetic
energy *can* be lost to heat, but this has to occur in a way that
conserves angular momentum.
--
spsystems.net is temporarily off the air; | Henry Spencer
mail to henry at zoo.utoronto.ca instead. | henry@spsystems.net

Posted by K. M. Kirby, esq. on September 30, 2006, 7:42 pm
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One of Saturn's moon's was recently recognized as having paleopoles.
Perhaps there are signs there of angular momentum being transferred &
conserved in the process.

One way I picture this as happening; if an iceball world finds itself
next to an emerging star or a heating-up gas giant, its equatorial
volatiles might vaporize -- with much of this "lost" mass recondensing
at the poles. Thus, areas at the poles may become much heavier,
possibly leading those spots to migrate towards the equator.

In extreme cases, might not such migration be seen to happen
repeatedly, perhaps along with increasing heat and burning off of
surface volatiles?


Henry Spencer wrote:
> >Regarding the current rotation speeds of the Moon and Mercury, is there
> >any possibility that these two objects had more spin velocity in the
> >distant past?
>
> It is essentially certain that they did, but the angular momentum was
> gradually transferred to either the parent body or the orbit via tidal
> interactions. (Similarly, Earth's rotational angular momentum is
> gradually being transferred to the Moon's orbit now, moving the Moon out
> and slowing the Earth. Eventually the Earth will end up with one side
> always facing the Moon, in the same way that one side of the Moon always
> faces the Earth -- see the Pluto-Charon system for an existing example.)
>
> >This question is related to another, and that is: does a freely
> >rotating planet lose some of its rate of spin for every geographical
> >readjustment occuring during true polar wander?
>
> Even postulating that "true polar wander" actually takes place, no.
> Angular momentum doesn't disappear. Moving mass outward from the axis of
> rotation slows the spin, *without* changing the angular momentum; if that
> mass then somehow gets moved back inward, the spin picks up again. The
> only way a planet can actually lose angular momentum is to transfer it to
> something else, e.g. as noted above.
>
> >This might make an interesting experiment for the ISS -- Having a
> >spinning globe, with an extra mass added near the pole, and observing
> >what happens to spin rate as the mass migrates to the equator of this
> >globe.
>
> This can be calculated without difficulty; there is no need to experiment.
> The physics of such shifts in rotation axis are well understood, not least
> as a consequence of experience with the dynamics of spinning satellites.
>
> >Does friction cause some of the rotational inertia to be lost to heat,
> >perhaps?
>
> "Rotational inertia" is not a well-defined quantity. The well-defined
> quantities involved are angular momentum and rotational kinetic energy,
> and it is important to distinguish between the two. Angular momentum, as
> noted above, can be transferred but cannot be lost. Rotational kinetic
> energy *can* be lost to heat, but this has to occur in a way that
> conserves angular momentum.
instead.


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