Suppose partial melting of the polar ice caps increases the moment of inertia of the Earth from 0.331MR^2 to 0.332MR^2. What is the change in length of day in seconds?

Question

Suppose partial melting of the polar ice caps increases the moment of inertia of the Earth from 0.331MR^2  to 0.332MR^2. What is the change in length of day in seconds?

bobpursley · Answer

momentum is conserved

Io*wo=In*wn

wn/wo=Io/Inew

but angular velocity=2PI/period

then
Periodorig/periodnwe=Io/In

period new= periodold*(..331/.332)
=24hrs*3600sec/hr*(.332/.331)

change in period
period new-period old
change in period=24*3600(.332-.331)/.331

I get about 260 seconds. check all that.