* Angular momentum* is the rotational analogue of linear momentum . For a particle rotating in a plane at radius about (see diagram below), its velocity component that is perpendicular to is

where is the period (time taken to complete a revolution) and is the ** angular velocity**.

The rotational kinetic energy of the particle is

where is the * moment of inertia*.

###### Question

What is moment of inertia and why is it equal to ?

###### Answer

The moment of inertia is the rotational equivalent of a particle’s inertia in linear motion. For a particle in linear motion, its inertia is quantified by its mass. For a particle in rotational motion, its inertia is dependent on both its mass and the distribution of that mass relative to (i.e. dependent on and for a point mass). Since , where is the angular velocity of the rotating particle, we define such that there is a correspondence between and , and between and .

Consequently, angular momentum, which is the rotational equivalent of linear momentum , is defined as:

Since a particle’s orbit may be circular or non-circular (see diagram above), its angular momentum is generally expressed as:

or equivalently,

Therefore, angular momentum is a ** pseudo-vector** with a direction indicated by the right-hand rule.