Earth and Rotational Mechanics

Earth and Rotational Mechanics:

Today lets deal with an application of rotational mechanics. What happens if polar ice cap melts ? Is there any changes to earth apart from global changes? For that we need to consider the following two stages carefully, stage 1: consider earth of mass M and radius R rotating with angular speed W. It has moment of Inertia I when its polar ice caps are not melt and present in NP and SP. Stage 2: It has moment of inertia Io when the polar ice cap melts and the water moves down to or near the equator, so the earth angular speed becomes Wo . 

Photo by NASA 

Let say we move from stage 1 to stage 2. Is there any external torque acting on this process as we move from stage 1 to stage 2 ? NOOO ! So we can conserve Angular Momentum between two instances.

So,

I W = Io Wo

But here I <  Io (why ??)

Answer to Why??

In stage 1 and 2, mass of ice cap remains same,say m. So, in stage 1 the mass of ice caps remain near axis, where as the mass of ice caps in stage 2 are near the equator (same mass at distance R from axis )? So which one will have greater Moment of inertia ?? Of-course in stage 2...

Stage 1

Stage 2

So the value of Wo < W to compensate the equality...

So if ice caps melt, the rotational speed decreases.

  

Experiment:

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Sit on a rotating chair with the arms intact carrying book in the both hands and ask your friend to rotate it. As you are in the motion, extend your arms on both side...What do you experience ? Comment us your observation ? How is this experiment related to the post dealt today ?