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Concern has been expressed that warming of the atmosphere, resulting from industrial pollution, could cause the polar ice caps to melt. If the polar ice caps of the earth were to melt and the water returned to the oceans, the oceans would be made deeper by about $12.2$ m. This will effect the earth's rotation. Make an estimate of the resulting change in the length of the day, assuming that all of the earth's surface is covered with oceans. Assume that the earth (excluding the polar ice caps) is a uniform sphere with a mass of $5.98 x 10^24$ kg and a radius of $6.37 \times 10^6$ m. In addition, assume that the polar ice caps do not contribute to the rotational inertia of the earth since they are located very close to the rotation axis.

From what I found out this the final formula

$$T_\text{after} = 24h \left( 1+ \dfrac53 \dfrac{M_\text{ice}}{M_\text{earth}}\right)$$

But I keep getting the wrong answer, or if not the right one what is the right one, show how it is done it will help a lot. Thanks

user179033
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  • I think you can conserve angular momentum here. Since external torque is not present. You will have $I\omega = const.$ Here $I$ is moment of inertia and $\omega$ is angular velocity. – jonsno Nov 09 '17 at 13:09
  • So the moment of inertia of a thin sphere is $\frac53$ of the moment of inertia of a homogenous ball of the same mass and radius? – Hagen von Eitzen Nov 09 '17 at 13:15
  • @Hagen I think its true https://en.wikipedia.org/wiki/List_of_moments_of_inertia – jonsno Nov 09 '17 at 13:22
  • How can you get the answer tho? Because I keep getting the wrong one? I would appreciate your help – user179033 Nov 09 '17 at 23:17

1 Answers1

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Conservation of angular momentum ($L=I\omega$). Look at the moment of intertia of Earth before and after adding $12.2 \text {m}$ of water to the oceans, and consider how $\omega$ must change in order for $L$ to remain unchanged.

Cargobob
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