- #1
simpleton
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Homework Statement
The polar ice caps contain about 2.3*10^19 kg of ice. This mass contributes essentially nothing to the moment of inertia of Earth because it is located at the poles, close to the axis of rotation. Because of Global warming, all the ice has melted and formed a uniform coat of water around the surface of the Earth. Calculate the change in the length of the day.
Given:
Mass of Earth = 5.98*10^24 kg
Radius of Earth = 6370 km
1 day = 86400s
Homework Equations
I of shell of sphere = 2/3*M*R^2
I of solid sphere = 2/5*M*R^3
The Attempt at a Solution
Actually, I have the solution to the problem, however, I don't agree with the solution, so I would like to know what you guys think.
Given Answer:
Assuming that Earth is a sphere before and after the melting of ice, and that the mass of Earth is M, the mass of ice is m, the radius of Earth is R, then we can formulate the following equation:
Initial I = 2/5*M*R^2
Final I = 2/3*m*R^2 + 2/5*M*R^2
Initial Time = 86400s
Final time to (Final I)/(Initial I)*T -T = 0.55s
However, I don't agree with the part for the calculation of the final I. I think it should be:
2/3*m*R^2 + 2/5*(M-m)*R^2
This is because you cannot count the mass twice in my opinion. However, they said that the ice does not contribute to the moment of inertia, so I am not sure how you go around handling this :(