Rolling, Torque, and Angular Momentum of Earth

[mb85]

Suppose that Earth's polar ice caps melted and the water returned to the oceans, so that the oceans were deeper by about 37 m. What effect would this have on Earth's rotation? Make an estimate of the resulting change in the length of the day. (Concern has been expressed that warming of the atmosphere resulting from industrial pollution could cause the ice caps to melt.)


RadiusEarth = Re + change in radius


IWtoday = IWmelt
L = IW
so as I increases, W decreases
W = 2pie/T
so as W decreases, T increases

W' = 2pie/T'
W = 2pie/T

W'/W
change in W = W' - W/W
so 1 - W'/W

change in L = 0 = change in (IW)
d(IW) = Idw + WdI

change in W/W = change in I/I

this is what we came up with, but it just seems like a lot of things that are potentially not important to the concept and that's confusing me. Can someone help me sort through this. Thanks.

 

[mb85]

can anyone help?

 

[Chi Meson]

If the oceans were 37 meters deeper, that means the Earth's radius would increase. By what percentage? And how would this increase in radius (with the same mass) change the moment of inertia? by what percentage?