(a) Assuming Earth to be a homogeneous sphere that has a radius r and a mass m, show that the period T (time for one daily rotation) of Earths rotation about its axis is related to its radius by where Here L is the magnitude of the spin angular momentum of Earth. (b) Suppose that the radius r changes by a very small amount, due to some internal cause, such as thermal expansion. Show that the fractional change in the period is given approximately by (c) By how many kilometers would r need to increase for the period to change by (so that leap years would no longer be necessary)?

7/22/2017 OneNote Online Lecture 2/10/14 Monday, February 10, 2:29 PM https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!1292&cid=36773184373a8f0b&app=OneNote&authkey=Ao_s2fF7RmzCCyQ 1/4 7/22/2017 OneNote Online https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!1292&cid=36773184373a8f0b&app=OneNote&authkey=Ao_s2fF7RmzCCyQ