# Why is momentum important in physics

## Momentum and angular momentum¶

### The angular momentum¶

In a similar way to how the description of translational movements was found to be helpful in the definition of the momentum, the introduction of a so-called angular momentum has also proven useful in the description of rotational movements.

The angular momentum of a body is dependent on its moment of inertia and its angular velocity and characterizes the force that this body exhibits during a rotational movement.

*Definition:*

The angular momentum of a body is equal to the product of its moment of inertia and its angular velocity :

The angular momentum is a vector quantity and points in the same direction as the angular velocity, i.e. perpendicular to the plane of rotation. The amount of angular momentum of a rotating body changes if either the amount of its angular velocity or its mass distribution and thus its moment of inertia changes.

Mathematically, the change in angular momentum can be expressed as follows:

This change in momentum can be in relation to time in which the change takes place. So it follows:

The term in the first part of this sum can be based on the context also as write. This term can be understood as torque and is identical to the change in the angular momentum, provided the change in the moment of inertia is zero. Otherwise, this must also be taken into account: [3]

A torque can therefore generally be understood as a change in the angular momentum over time.

The law of conservation of angular momentum

A system of several interacting bodies has a total angular momentum, which corresponds to the sum of all individual angular momentum:

If no external torques act on the system, then the total angular momentum is constant. This empirically found fact is called the conservation of angular momentum and, together with the conservation of momentum and the conservation of energy, represents one of the most important conservation laws in mechanics.

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