# What is angular momentum? Derive an expression for the angular momentum of a rotating body.

16.9k views
in Physics

What is angular momentum? Derive an expression for the angular momentum of a rotating body.

by (51.1k points)
selected by

The angular momentum of the particle is defined as the moment of momentum about the axis of rotation.

∴ Angular momentum = linear momentum x perpendicular distance from the axis.

If ω is the angular velocity of the particle, then the linear velocity v = r ω.

∴ Angular momentum of each particle = (mv)r = (mrω) r = mr2ω.

∴ Total angular momnetum of the body is L = (Σ mr2ω) = (Σ mr2)

ω = lω where l = Σ mr2.