Question

If polar ice caps melts, then the angular rotation of the earth :
A) increases
B) decreases
C) remains constant.
d) depends on when the ice melts.

Answer 1

Hint: Use the Concept of Moment of inertia(I) as we move away or towards the centre (in this case equator to pole or pole to equator) .

Step by Step Solution
 Earth can be considered as a sphere.Now, if ice in the polar region melts,the resulting water will flow towards the equator and consequently moment of inertia(I) of the earth will increase as more mass has accumulated at the equator which is more distant from the rotational axis as compared to the poles.So, from the law of Conservation of Angular Momentum (COAM) we have -

             $Iw$= constant (where I= moment of inertia and w= angular velocity)

We can see that if I will increase w has to decrease to keep the value constant.

In this case , as I increases w has to decrease and hence angular velocity decreases when ice melts at polar region.

Note
 1) If the moment of inertia increases, then angular velocity decreases (Iw= constant).
2) Time period increases ($T = \dfrac{{2\pi }}{w}$). Since the time period increases, the duration of the day becomes longer.
3) The condition of zero net angular impulse is required for conservation of angular momentum.
4) Other examples of conservation of angular momentum are -
     a)Spinning ice skater.
     b)Student on rotating turntable.