You can get the moment of inertia of a uniform rod by integration and we did for a solid disk, but let's do it in a more tricky way using the parallel axis theorem. It's neat because it doesn't take much calculation, but you have to think about the problem!
We've seen a lot of examples, and we know the final answer has to be of the form
where we want to determine C. What if we rotate the rod about an end intead? Then the parallel axis theorem tells us that
We still don't know C so why does this help? Because we can get a different formula for this a different way. If instead of shifting the axis, we chop off the left half of the rod, then the new moment of inertia is
So this is the moment of inertia of a rod of length L/2 and mass M/2 rotating on it's end.
What will be the moment of of a rod twice the length? We want
to know this because it's the same as 
. Well
then 
and 
. So from the
last formula this is
Comparing this with our first formula for , eqn. 1.67
we have
Solving for C we can just cancel the 
's, obtaining
. Therefore from eqn. 1.66 we have
