# What Is Kinetic Energy?

Kinetic energy or motion energy is a form of energy that a body has in motion due to the inertia of mass. In non-relativistic frames of reference, kinetic energy is directly proportional to the mass and the square of the velocity. It is the same as the work that needs to be done to move the body from the resting state to the condition it is in. In classical mechanics we make the following considerations:

• A body with mass m that moves at a speed v has a kinetic energy Ec = (m · v 2 ) / 2.
• If the body also rotates around the center of mass, it will have kinetic energy as a result of this rotation. Ec = (I · w 2 ) / 2. In the equation above I is the inertia of the body and w is the angular velocity.
• With a general movement, the König theorem is applicable, and the total kinetic energy is the sum of the kinetic energies of both movements.

## Energy Conversion

The total kinetic energy of a system can, for example, change when converted to or from potential energy, by converting chemical energy in an internal combustion engine, including a rocket motor, and by firing a projectile, and by heat or energy. thermal, in case of friction or collision.

The speed, and therefore also the kinetic energy, depends on the chosen inertial system. The total kinetic energy of a system is less when the center of mass of that system is at rest. In other cases, the kinetic energy corresponding to the movement of the total mass is added to the speed of the center of mass.

The speed of the center of mass of a closed system remains constant due to the law of conservation of the moment. The changes in the total kinetic energy of the system as in the previous examples therefore depend not on the inertial framework, but the changes in the parts of the system do.

For example, if two bodies attract each other and their separation becomes smaller, the potential energy is converted into kinetic energy. Depending on the inertial system, this increase in kinetic energy increases differently for each of the two bodies. Even the kinetic energy of one body can decrease, increasing the energy of the other.

Similarly, if a rocket converts chemical energy into kinetic energy, then it depends on the speed of the rocket (and therefore the inertial system) to what extent this increase in total kinetic energy benefits the rocket and to what extent the mass of reaction and the kinetic energy of the rocket can even decrease, increasing the reaction mass, or vice versa.

With a die, in the case of a fully elastic central collision, the transmitted kinetic energy depends on the inertial system as follows: this energy is proportional to the speed of the center of mass of the colliding objects.

## Kinetic Translation Energy

The total kinetic translational energy of two bodies relative to the center of mass can be calculated based on the reduced mass and the mutual velocity, see the two-body problem. The distribution of this energy between the two bodies is inversely proportional to the mass.

For example, with the system of a moving car and the rest of the Earth, the kinetic energy of the rest of the Earth hardly changes with the speed changes of the car, although the momentum always changes to the same extent as the car.

In the case of a three-body problem with the Sun, Earth, and a space capsule, the Sun's kinetic energy relative to the center of mass of all three bodies is also negligible. Changes in the kinetic energy of the Earth through interaction with the capsule are now not negligible in relation to the kinetic energy of the capsule, see also the escape rate.

## The Kinetic Energy in the Molecules

The total kinetic translational energy of local molecules is the sum of, on the one hand, the kinetic energy corresponding to the movement of the total mass of these molecules at the speed of their center of mass (i.e. macroscopic movement) and, on the other hand, the kinetic translational energy relative to the center of mass. The latter is related to the temperature at the corresponding location.

With an ideal gas, the kinetic translation energy relative to the center of mass is a total of 3/2 times the pressure multiplied by the volume and proportional to the temperature, namely 12.47 J per mole per Kelvin. The latter is 3/2 times the gas constant, and in single-atom molecules it is equal to the specific heat in constant volume.

With multi-atom molecules, there is another energy that increases with temperature, namely, that of the rotation and vibration of the molecules, making the specific heat higher.

At the same temperature (and in particular also in a gas mixture), heavy molecules have on average the same kinetic translation energy as light (equipartition theory); Therefore, they have a lower speed.

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Published: May 8, 2019
Last review: May 8, 2019