Question

Is angular momentum equal to Inertia times Omega and why?

Answer 1

see below

Explanation:

Angular momentum is also known as the moment of momentum

consider a rigid body rotating about a fixed axis with angular velocity of `omega`, whose moment of inertia is `I`

the definition of `I` is the sum of the products of the mass and the square of the perpendicular distance to the axis of rotation of each particle in a body to the axis of rotation.

ie

`I=summr^2"`

consider the rigid body is made up from particles each of mass `m`

then the moment of momentum ( call it `L`) of each particle

`L =" momentum "xxr`

`" where " r " is the perp. distance from the axis"`

`:.L=mvr`

where `v` is the linear (tangential) velocity

but for angular motion

`v=romega`

so

`L=mrromega=mr^2omega`

For the total angular momentum we have to sum up all the particles

`L_T=sum mr^2omega`

`L_T=omegasummr^2`

`L_T=Iomega`

so angular momentum is moment of inertia `xx`omega

in vectors the formula is

`vecL=vec r xx mvecv`