To determine the angular momentum in circular motion, one must multiply the moment of inertia by the angular velocity.

Angular momentum is a vector quantity that characterizes the rotational motion of an object. In the context of circular motion, angular momentum is computed using the relationship:

where $L$ represents the angular momentum, $I$ denotes the moment of inertia, and $\omega$ signifies the angular velocity.

The moment of inertia quantifies an object’s resistance to changes in its rotational motion and is influenced by both the object’s mass and the distribution of that mass relative to the axis of rotation. The units of angular momentum are expressed in kg m²/s, the moment of inertia is measured in kg m², and angular velocity is given in radians per second.

For a circular object, the moment of inertia can be calculated using the formula:

where $m$ is the mass of the object and $r$ is the radius of the circle. For more complex shapes, the moment of inertia can be determined through the process of integration.

In summary, to find the angular momentum in circular motion, utilize the formula:

Calculate the moment of inertia using $I = mr^2$ for circular objects or apply integration methods for objects with more intricate shapes.