Why is the length L divided by 2 in physical pendulum calculations?

[calgal260]

physical pendulum--thin rod

Why do you have to divide the length L by 2 in these cases? The explanation that's provided in my book says "the distance L between the pivot and the center of gravity is .5 the length L."

This makes no sense whatsoever. The length should be the same regardless of where you measure it from, be that from the center of the gravity or not.

 

[flatmaster]

Taking L/2 accounts for where the actual mass is. If you had a single mass on a string, you would use L. Other shapes require more complicated adjustment than the L/2.