# Energy – calculating kinetic energy

This physics tutorial shows how to calculate the kinetic energy*. The prerequisite for this is a basic knowledge of the concept of energy.
In the following the term of the kinetic energy is to be explained, before it continues with the computation.

## What is kinetic energy?

The kinetic energy Ekin, also called kinetic energy, is a measure of how much work has to be done on a body to bring it from rest to a certain state of motion. It is influenced by the mass m and the velocity v of this body.

##### Calculating the kinetic energy of a mass m with velocity v

Kinetic energy is a state variable. This means that it depends exclusively on the current state of the system under consideration and is therefore completely independent of the path to reach this state.

Kinetic energy is inherent in the state of motion of a body. It changes proportionally to the square of the velocity v and the mass m, measured at the inertial system in which the body is described.

Accordingly, the amount of kinetic energy depends on the point of view from which the system is viewed. Often an inertial system is used for this, which is at rest in relation to the ground.

Formula symbol: Ekin

Unit: J (Joule) = Nm (Newton-meter) = kg-m 2 -s -2

## Formula for calculating kinetic energy

The speed v is related to the respective reference system. The driver of a moving passenger car has a kinetic energy of Ekin = 0 J. If, on the other hand, the road serves as the reference system for calculating kinetic energy, both the driver and the car have a kinetic energy Ekin> 0 J.

### Calculate kinetic energy – formula:

The dependence of the kinetic energy on the square of the speed v plays among other things with car accidents a role not to be underestimated. For example, doubling the speed v also means quadrupling the kinetic energy Ekin.

### Kinetic energy of rotating bodies

Expanded bodies can not only perform a translational motion, but also a rotational motion. The kinetic energy contained in the rotary motion is called rotational energy. This is proportional to the moment of inertia of the body and to the square of the angular velocity.

## Calculate kinetic energy – example:

Now we come to a small task for the calculation of kinetic energy.

A car with a mass m = 1000 kg travels at a speed v = 50 km/h. How large is the kinetic energy Ekin of the vehicle compared to the road? The equation for calculating kinetic energy Ekin is:

To calculate kinetic energy, first convert the speed v = 50 km/h into meters per second (SI unit of speed).

Now, to calculate the kinetic energy Ekin, the speed v and the mass m are inserted into the formula.

Result:

The kinetic energy Ekin of a car traveling at 50 km/h with respect to the road is 96465 J = 96.47 kJ.

What kinetic energy is and how to calculate kinetic energy* should now be clear to everyone. Other tasks on the subject can of course be considerably more complex, but the basic knowledge is already a prerequisite for mastering tasks of a higher degree of difficulty.