Momentum is a physical quantity used to describe the movement of a body. Impulses take place all the time in life, for example in sports such as tennis, football or billiards. In this article we will explain to you what constitutes the impulse and how it can be influenced and changed.

## Momentum (Physics) – Definition

As a first step, let’s look at the definition of physical momentum to get a feeling for the importance of this quantity.

Of the **pulse **is a physical quantity used to describe the movement of a body. Momentum describes the mass, direction and speed of a body.

In the case of momentum, the body under consideration is regarded as a mass point. This means that, in theory, all mass is stuck in a single imaginary point. A translational movement starts from this point.

In a translational movement, every single point of a rigid body experiences the same displacement.

Using examples from reality, we can see that the impulse does not only consist of the translational movement! Can you think of a scenario straight away?

Take a look at throwing a bowling ball, for example!

When a bowling ball is thrown, it rolls across a surface. On the one hand, the ball moves in a straight line towards the cones. On the other hand, it also rotates around its own center.

If momentum is a physical quantity to describe the movement of a body and the bowling ball makes two movements in total, then there must be two different momenta, right?

Indeed that is true! The bowling ball is one **translational motion** exposed when it rolls towards the cones and, on the other hand, to a rotating movement around its own axis. These are also called in physics **rotational movement**.

The translational movement is described by the simple impulse and the rotational movement by the so-called **angular momentum**.

We will look at the exact formulas for momentum and angular momentum later in the article. But first take a look at the following problem. Can you distinguish between momentum and angular momentum?

**task**

Which of the following examples is momentum and which is angular momentum?

- tennis ball
- Rotor blades of a helicopter
- spinning top
- rolling billiard ball
- moving car

**solution**

- The tennis ball has momentum as it flies through the air.
- The rotor blades rotate around their own centre, hence angular momentum
- Rotation around its own axis, angular momentum
- Momentum and angular momentum are correct, there are two motions in rolling over a surface.
- The car itself has momentum (the tires would have angular momentum and momentum again)

Of course, you can also express the momentum in a formula. You will now find out how this works.

## Momentum (physics) – formula

The momentum is calculated by multiplying the mass m with the velocity v. Mathematically formulated, the following definition results:

The general definition of **pulse **reads:

the **Unit **of momentum is given in Newton seconds:

In most cases, the mass remains unchanged and can therefore not cause any change in momentum. Only the speed can be influenced, and for that one must **force on the body**.

the **force required for momentum change** can be calculated from the quotient of the momentum change * *and the change in time required for this * *to calculate:

In order to achieve a higher momentum, acceleration work must be done. To do this, kinetic energy must be added to the system.

You can calculate the kinetic energy with .

By plugging in the definition of momentum, you now have another formula to calculate the **kinetic energy** to determine:

You have to be careful to distinguish between momentum and kinetic energy. Both quantities are made up of mass and speed, but momentum is a directional quantity! The kinetic energy is undirected because the amount of speed is included here.

Most momentum changes in classical mechanics take place through collisions. You can see in the table below which ones are available and where you can find them in everyday life!

**shock type****definition****situation in everyday life****elastic shock**Bodies repel each other and no kinetic energy is lost.

**inelastic collision**Bodies repel each other, but deform, part of the kinetic energy is converted to internal energy. The bodies deform when hit and the bodies are subject to heat generation

**inelastic collision** Plastic deformation in which the bodies become one after the collision and large amounts of kinetic energy are converted into internal energy. The deformation of the bodies is now irreversible and they are subject to a very high heat build-up.

Independent of these collisions, there is another important form of momentum: angular momentum.

### angular momentum

Angular momentum describes a movement in which there is a circular movement around its own center of mass.

The angular momentum * L* is calculated with the formula:

In some cases, the momentum is also calculated using the angular velocity:

With :

If you want to know details about angular momentum then you are welcome to visit .

Momentum also plays a role in** special theory of relativity**. Any body with a mass greater than 0 is given as follows:

Bodies at rest have no speed and therefore no momentum

But they have a resting energy, which is provided by the famous formula

can be calculated. Objects without mass (such as photons) move at the speed of light. This in turn follows

Now you know what an impulse and a push is in general. The following is an important basic rule in physics: conservation of momentum.

## conservation of momentum

In a closed system, the sum of all momenta remains the same as long as no additional force is applied.

You can easily imagine this using the example of two billiard balls. One ball is stationary, the other is moving. The balls collide and the momentum is transmitted. Now the previously moving ball no longer moves, but the previously stationary one does. Therefore, conservation of momentum in physics is defined as follows:

The total momentum before a collision is equal to the total momentum after a collision:

In the following task you can try to prove the law of conservation of momentum using an example from reality.

**task**

Ball 1 with the mass and the speed collides with the second ball 2, which is at rest and has the same weight (). Show that the law of conservation of momentum applies to elastic collisions, using the velocities of the spheres after the collision.

**solution**

To find the momentum before the shot, we use the above formula for each individual ball and add the momenta to get a total momentum:

After the impact, ball 1 no longer moves with the mass and remains stationary, while ball 2 that was struck moves with it.

This solution proves that the total momentum before the collision is equal to the total momentum after the collision.

## Impulse Physics – The Most Important

- Momentum is a physical quantity used to describe movement
- Momentum is made up of mass and velocity

- The impulse is given in units of Newton seconds

- The momentum has a direction and is therefore called a vector quantity
- The law of conservation of momentum applies in closed systems and states that the sum of all momenta before a collision is equal to the sum of all momenta after the collision