Angular Momentum and Moment of Inertia

The turning movement of a particle about the axis of rotation is called the angular momentum of the particle. It is measured as the product of the linear momentum and perpendicular distance of its line of action from the axis of rotation.

It is denoted by $\displaystyle L$.

Angular Momentum Formula

The formula of angular momentum is

angular momentum = linear momentum × perpendicular distance from the axis of rotation

i.e. $\bbox[15px, #e4e4e4, border: 2px solid #000000]{\boldsymbol {\displaystyle L=r\times p=m\left( {r\times v} \right)}}$

where r is the position vector of the particle with respect to O. As the particle moves relative to O, in the direction of its linear momentum p (= mv), position vector r rotates around O.

The formula in terms of moment of inertia is

angular momentum = moment of inertia × angular velocity

i.e. $\bbox[15px, #e4e4e4, border: 2px solid #000000]{\boldsymbol {\displaystyle L=I\omega}} $

where I is the moment of inertia and $ \displaystyle \omega $ is the angular velocity.