- #1
Jomaho
- 2
- 0
Homework Statement
Question requires assumption that the Earth is spherical, all the ice is located at the axis of rotation.
Basically if all the ice was to melt uniformally over the surface of the earth, what would be the change in the length of the day?
Mass of ice: m= 2.3*10^19 kg
Mass of earth: M= 6.4*10^24 kg (doesn't say whether this takes into account the ice, I assumed it does)
Homework Equations
Moment of inertia of a solid sphere: I=2m(r^2)/5
Moment of inertia of a spherical shell I=2m(r^2)/3
m=mass
r=radius
The Attempt at a Solution
I went about it as follows:
Initially: I1=2M(r^2)/5
After: I2=2(M-m)(r^2)/5 + 2m(r^2)/3
I then used conservation of momentum:
L= I1w1 = I2w2
Finally using:
Time diff = 2*pi*((1/w2)-(1/w1))
Where 2*pi/w1 = 24hours
This eventually canceled down to:
Time diff = (4*pi*m)/(3*w1*M)
I got the answer to be 0.621s. Would someone mind checking my method and answer?