# Kinetic energy

The kinetic energy or energy of movement is a form of energy that has a body in motion due to mass inertia. In non-relativistic frames of reference, the 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 so that the body goes from the state of rest to the condition in which it is found.

In classical mechanics we make the following considerations:

- A body with mass m that moves at a velocity v has a kinetic energy Ec = (m · v
^{2}) / 2. - If the body also undergoes a rotation around the center of mass, it will have a kinetic energy as a result of this rotation. Ec = (I · w
^{2}) / 2. In the above equation 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 into an internal combustion engine, including a rocket engine and firing a projectile, and 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 lower when the center of mass of that system is at rest. In other cases, the kinetic energy that corresponds to the movement of the total mass to the velocity of the center of mass is added. The velocity 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 frame of inertia, but 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 to 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 completely elastic central collision, the transmitted kinetic energy depends on the inertial system as follows: this energy is proportional to the velocity of the center of mass of the objects in collision.

## Kinetic translation energy

The energy of total kinetic translation of two bodies in relation to the center of mass can be calculated on the basis of the reduced mass and the mutual velocity, see the problem of two bodies. 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 changes in speed of the car, although the impulse always changes in the same measure as the automobile.

In the case of a three-body problem with the Sun, Earth and a space capsule, the kinetic energy of the Sun in relation to the center of mass of all three bodies is also negligible. The changes in the kinetic energy of the Earth through the 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 translation 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 velocity of their center of mass (ie, macroscopic motion) and, on the other hand, the energy of kinetic translation relative to the center of mass. The latter is related to the temperature in 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 the molecules of a single atom it is equal to the specific heat in constant volume. With the molecules of several atoms, there is another energy that increases with temperature, namely, the rotation and vibration of the molecules, so that the specific heat is greater.

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

Last review: May 8, 2019

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