Is angular momentum equal to Inertia and why?

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Angular momentum is also known as the moment of momentum
consider a rigid body rotating about a fixed axis with an angular velocity of , 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.

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

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

where r is the perp. distance from the axis

where v is the linear (tangential) velocity

but for angular motion


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

so angular momentum is moment of inertia omega in vectors the formula is

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