[This was brought up on PHYSHARE-L as well, and I still don't get how
rotational momentum is conserved. I realize that when I fully understand
it, I am going to feel like an idiot, but here goes....]
If the energy that is used to light the bulbs, etc., comes from the
earth's rotation, then the earth needs to lose kinetic energy. KE of a
rotating body is KE = 1/2 (rotational inertia) (rotational velocity)^2. I
presume that the actual shape of the earth doesn't change, so its
rotational inertia remains constant. That means that rotational velocity
must decrease.
On the other hand rotational momentum = rotational inertia x rotational
velocity . If rotational inertia stays the same and rotational velocity
decreases, then rotational momentum must get smaller. If rotational
momentum of the earth gets smaller, then the L of something else must get
larger.