Is angular momentum equal to inertia times angular velocity and why?

Yes, angular momentum ($L$) is equal to the moment of inertia ($I$) times the angular velocity ($\omega$) for a rigid body rotating about a fixed axis. This relationship is expressed as:

$$L=I\cdot \omega$$

### Explanation:

- **Angular Momentum ($L$)**: This is a measure of the rotational motion of an object. It depends on both how fast the object is spinning (angular velocity) and how the mass is distributed around the axis of rotation (moment of inertia).

- **Moment of Inertia ($I$)**: This is a measure of how the mass of an object is distributed relative to the axis of rotation. It's analogous to mass in linear motion but takes into account how far the mass is from the axis of rotation. For a given axis, the moment of inertia is defined as:

$$I=\sum m_i{r}_i^2$$

where $m_i$ is the mass of a small element of the object and $r_i$ is the distance of that element from the axis of rotation.

- **Angular Velocity ($\omega$)**: This is the rate at which the object rotates around the axis.

### Why this relationship holds:

The relationship $L=I\cdot \omega$ holds because angular momentum is essentially the rotational equivalent of linear momentum. In linear motion, momentum $p$ is the product of mass $m$ and velocity $v$:

$$p=m\cdot v$$

Similarly, in rotational motion, angular momentum is the product of the moment of inertia (the rotational equivalent of mass) and angular velocity (the rotational equivalent of linear velocity).