What is the expression for Angular momentum of a Rigid body rotating about an axis?

A rigid body rotates about a fixed axis. The rigid body consists of a large number of particles.
Let m1, m2, m3 etc., be the masses of the particles situated at distances r1, r2, r3 , … etc., from the fixed axis. All the particles rotate with the same angular velocity, but with different linear velocities depending on the values of ‘r’.
The angular momentum of a rigid body (L) = m₁ r₁²ω ₊  m₂ r₂²ω…
The angular momentum of a rigid body (L) = (m₁ r₁² + m₂ r₂²….) ω

The angular momentum of a rigid body (L) = Σ mr²ω …………………(1)

But, Σmr² = moment of inertia of the rigid body = I

Therefore,

Angular momentum of a Rigid body = I × ω……putting value of I in (1)

Angular momentum of a Rigid body = moment of inertia of the rigid body ( I) x × angular velocity (ω)

The S.I. unit for angular momentum is kgm²rad/s or kgm³/s