physics question #85



Fred Bucheit, a 55 year old male from the Internet asks on November 1, 1999,

Q:

How does mass shifting affect Earth's rotation? Could melting of polar icecaps cause a change in rotation?

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the answer

Jess Brewer answered on November 1, 1999, A:

A general theorem states that an object with three different principal axes to its inertia tensor will spin in a stable manner about its long or short axes but not about its intermediate axis. You can demonstrate this easily by attempting to spin a book or a chalk eraser. If a satellite was spinning about its long axis and then changed the moment of inertia about that axis, it would run into trouble when it reached the intermediate axis. Melting the ice caps would cause the Earth's rotational period to slow down by something in the neighbourhood of a second, if I recall. It's not that difficult to calculate, just remember that angular momentum L is conserved, L=Iomega where I = moment of inertia about the axis of rotation and omega is the rotational frequency; then take the mass of the ice caps and make a spherical shell out of it, calculate that shell's I and add it to the present Earth's I and figure out by what fraction omega must decrease to compensate. I don't think this will cause an axis shift, though. Too small. And whatever else happens, the net L of the Earth can't change unless we get hit from outside.

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