# Comparing 2 formula derivations

1. Oct 6, 2009

### Vykan12

Here is how my book goes about defining the moment of inertia.
Now here's how my book goes about deriving an expression for the angular momentum of a rigid body.
From this the book derives that L = Iw
My question is in regards to the bolded part. How come in one derivation we assume r_i is a measure of the perpendicular distance from the axis of rotation, and in the other we made no such distinction, but rather considered r_i a 3-D vector?

2. Oct 9, 2009

### Vykan12

My physics teacher answered this for me.

The only reasons the derivations are different regarding r_i is because inertia isn't a vector whereas angular momentum is.