Relation between angular momentum and moment inertia:

Let us consider that a rigid body consists of a large number of particles of masses $m_1$, $m_2$, $m_3$, etc., rotating about a fixed axis $O_1O_2$ with a uniform angular velocity $\omega$. Let $r_1$, $r_2$, $r_3$, etc. be the distances of the masses $m_1$, $m_2$, $m_3$, etc respectively from the axis of rotation. Since the rigid body rotates with a uniform angular velocity, so all the masses also rotate with the same angular velocity. So the linear momentum of the particle of mass $m_1$ is $m_1r_1\omega$.

Therefore the moment of momentum of $m_1$ about the axis of rotation is $m_1r_1\omega\times{r_1}=m_1{r_1}^2\omega$. This is also known as angular momentum.
The angular momentum of mass $m_2$ about the axis of rotation is $m_2{r_2}^2\omega$, of mass $m_3$ about the axis of rotation is $m_3{r_3}^2\omega$ and so on.
So the angular momentum of the whole rigid body is given by,
$L=m_1{r_1}^2\omega+m_2{r_2}^2\omega+m_3{r_3}^2\omega+\cdots\\=(m_1{r_1}^2+m_2{r_2}^2+m_3{r_3}^2+\cdots)\omega\\=(\sum{mr^2})\omega\\=I\omega$
where, $I=\sum{mr^2}$ is the moment of inertia of the body about the axis of rotation.