- #1
Vykan12
- 38
- 0
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?
To begin, we think of a body as being made up of a large number of particles, with masses m_1, m_2, ... at distances r_1, r_2, from the axis of rotation. [...] The particles don't necessarily all lie in the same plane, so we specify that r_i is the perpendicular distance from the axis to the ith particle.
Now here's how my book goes about deriving an expression for the angular momentum of a rigid body.
We can use eq (10.25) to find the total angular momentum of a rigid body rating about the z axis with angular speed w. First consider a thing slice of the body lying in the xy plane.
From this the book derives that L = Iw
We can do the same calculation for other slices of the body, all parallel to the xy-plane. For points that do not lie in the xy-plane, a complication arises because the r vectors have components in the z direction as well as the x and y directions.
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?