# Weird Global Warming

## Homework Statement

I swear this is the weirdest question I've encountered: If the South polar ice cap melts completely due to global warming, then what do you expect to happen to the length of the day?

2.Choices
a. It will get slightly longer
b. It will get slightly shorter
c. It will not change, but the year will slightly change length
d. It will only change if the North polar ice also melts
e. there will be no change at all

berkeman
Mentor

## Homework Statement

I swear this is the weirdest question I've encountered: If the South polar ice cap melts completely due to global warming, then what do you expect to happen to the length of the day?

2.Choices
a. It will get slightly longer
b. It will get slightly shorter
c. It will not change, but the year will slightly change length
d. It will only change if the North polar ice also melts
e. there will be no change at all

You should know by now that you are required to show your own work before we can offer tutorial help.

What do you think are the best choices, and why? If the polar cap melts, what happens to the mass and its distribution? What effect(s) would that have?

a. It will get slightly longer
b. It will get slightly shorter
c. It will not change, but the year will slightly change length
d. It will only change if the North polar ice also melts
e. there will be no change at all

Sure. Well here's my analysis. The length of the year depends on how fast the earth revolves around the sun, even after the ice cap melts, the mass of the earth should remain unchanged and so earth's revolution should remain unchanged, so c is probably wrong. The length of the day is dependent on how fast the earth rotates on its axis, the south ice cap is enormous, originally all the mass of the ice is at the south pole, melting leads to this mass being distributed across the earth, so the moment of inertia of the earth may increase, leading to slower rotation and a slightly longer day?

That's my best guess.

berkeman
Mentor
a. It will get slightly longer
b. It will get slightly shorter
c. It will not change, but the year will slightly change length
d. It will only change if the North polar ice also melts
e. there will be no change at all

Sure. Well here's my analysis. The length of the year depends on how fast the earth revolves around the sun, even after the ice cap melts, the mass of the earth should remain unchanged and so earth's revolution should remain unchanged, so c is probably wrong. The length of the day is dependent on how fast the earth rotates on its axis, the south ice cap is enormous, originally all the mass of the ice is at the south pole, melting leads to this mass being distributed across the earth, so the moment of inertia of the earth may increase, leading to slower rotation and a slightly longer day?

That's my best guess.

That would be my take on the question as well. Good reasoning. Do you know if it's right?

actually I don't know if it's right.

more importantly though, I think this question is probably exaggerated to emphasize the physical concepts of rotation and gravitation...but realistically, the melting of ice caps will not affect (or is too insignificant to affect) the rotation of the earth right?

berkeman
Mentor
actually I don't know if it's right.

more importantly though, I think this question is probably exaggerated to emphasize the physical concepts of rotation and gravitation...but realistically, the melting of ice caps will not affect (or is too insignificant to affect) the rotation of the earth right?

Agreed. Very insignificant.