Table of Contents

## Momentum: Definition

Momentum is a vector quantity, which is used to describe the motion of an object, and its direction is parallel to the motion of that object.

** p = m * v**

p ⇒ momentum [kg * m/s], [N * s]

m ⇒ mass [kg]

### The Law of Momentum Conservation

The law of momentum conservation states that in an isolated system, which does not have any interaction with its environment, all momentum is constant. So when two objects collide, the total momentum of these two objects before the collision is equal to their total momentum after the collision.

### Impulse

Impulse can be defined as the change over time in momentum, caused by an average force. It is defined as follows:

I^{→}^{ }⇒ impulse [kg * m/s]

F_{av} ⇒ average force [N], [kg * m/s2]

p ⇒ momentum

Δt ⇒ duration of impulse

### Moment of Inertia

A static/rigid body has resistance. Once a force sets a rigid body in rotating motion, a moment of inertia occurs. It depends on the body’s mass distribution in relation to the axis.

J ⇒ moment of inertia [kg * m^{2}]

r ⇒ axis of rotation

ρ ⇒ mass distribution

### Angular Momentum

Angular momentum refers to what colloquially might be called swirl or spinning. It describes the direction and speed of a rotation about an axis, and it increases

- the bigger the mass of the body is;
- the higher the velocity of the body is;
- the longer the distance from the axis is.

It is defined by the following equation:

**L = r * p**

## Collisions

### Central Collision

**Δp ⇒ collision [(kg * m)/s]**

Collision can be defined as a change in momentum over time and can be described by the following equation:

**Δp = F * Δt**

One can distinguish two types of collision:

- Elastic collision: Kinetic energy is conserved.
- Inelastic collision: A part of the kinetic energy is converted into internal energy.

If the centers of gravity of the colliding bodies move along a straight line, such collision is defined as a straight-line central collision.