How Would Melting Polar Ice Caps Affect Earth's Day Length?

[zoner7]

Homework Statement

If the melting of the polar ice caps were to raise the water level on the Earth by 10m, by how much would the say be lengthened? Assume the moment of inertia of the ice in the polar ices caps in negligible (they are very near the axis), and assume that the extra water spreads out uniformly over the entire surface of the Earth (that is, neglect the area of the continents compared with the area of the oceans). The moment of inertia of the Earth(now) is 8.1 X 10&37 kg m^2.

The Attempt at a Solution

good luck... I have no idea how to even go about doing this. I know that i need to examine the radius increase of the Earth do to the water level changing, but since I can't look up any values that aren't given to me, I really have no idea where to even start. if anyone has even the slightest inkling of what to do, I'd love to hear it.

thank you in advance

hmm I suppose that the moment of intertia of a sphere is key:

2/5 MR^2
We can set 2/5 MR^2 = x.

we know that this increases to 2/5 M(R + 10m)^2.

Then the change in the moment of inertia would be equal to [2/5 M(R + 10m)^2 - x], or 8.1 X 10&37 kg m^2 - x.

That's one step down :)

 

[LowlyPion]

Homework Statement

If the melting of the polar ice caps were to raise the water level on the Earth by 10m, by how much would the say be lengthened? Assume the moment of inertia of the ice in the polar ices caps in negligible (they are very near the axis), and assume that the extra water spreads out uniformly over the entire surface of the Earth (that is, neglect the area of the continents compared with the area of the oceans). The moment of inertia of the Earth(now) is 8.1 X 10&37 kg m^2.

The Attempt at a Solution

good luck... I have no idea how to even go about doing this. I know that i need to examine the radius increase of the Earth do to the water level changing, but since I can't look up any values that aren't given to me, I really have no idea where to even start. if anyone has even the slightest inkling of what to do, I'd love to hear it.

thank you in advance

hmm I suppose that the moment of intertia of a sphere is key:

2/5 MR^2
We can set 2/5 MR^2 = x.

we know that this increases to 2/5 M(R + 10m)^2.

Then the change in the moment of inertia would be equal to [2/5 M(R + 10m)^2 - x], or 8.1 X 10&37 kg m^2 - x.

That's one step down :)

I'd have to wonder if a more useful approach wouldn't be to calculate the moment of a 10 m hollow sphere of water at the radius of the earth. (Calculate the surface area of Earth times 10 m times mass of water to get the mass.) Then add that to the known moment of the Earth to arrive at the total moment.

Because the mass of the water won't be as much as the weight of the magma based densities of the landmass.

Since angular momentum needs to be conserved ... you can get to the change in rotation.

 

[CampyPython]

I still could not reach the answer, please can you explain more?