kinetic energy - Simple explanation, Definition, In Newtonian mechanics, In relativistic mechanics, In quantum mechanics

Energy associated with an object's motion; a scalar quantity; symbol K, units J (joule). For an object of mass m moving with velocity v, kinetic energy K = mv²/2. A change in kinetic energy is work done to the object by a force.

Energy Portal

Kinetic energy is the energy that a body possesses as a result of its motion. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

Under certain assumptions, this work (and thus the kinetic energy) is equal to:

where m is the object's mass and v is the object's speed.

Simple explanation

Energy can exist in many forms, for example chemical energy, heat, electromagnetic radiation, potential energy (gravitational, electric, elastic, etc.), nuclear energy, rest energy and kinetic energy.

These forms of energy can often be converted to other forms. Kinetic energy can be best understood by examples that demonstrate how it is transformed from other forms of energy and to the other forms. The energy has been converted into the energy of motion, known as kinetic energy but the process is not completely efficient and heat is also produced within the cyclist.

The kinetic energy in the moving bicycle and the cyclist can be converted to other forms. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated as heat energy.

See also energy conversion.

Simple calculation

In classical mechanics, the kinetic energy of a "point object" (a body so small that its size can be ignored) is given by the equation where m is the mass and v is the speed of the body.

For example - one would calculate the kinetic energy of an 80 kg mass traveling at 18 meters per second (40 mph) as joules.

Note that the kinetic energy increases with the square of the speed.

More simple examples

Spacecraft use chemical energy to take off and gain considerable kinetic energy to reach orbital velocity.

Kinetic energy can be passed from one object to another.

Flywheels are being developed as a method of energy storage (see article flywheel energy storage).

Definition

This equation states that the kinetic energy (Ek) is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal change of the body's momentum (p).

In Newtonian mechanics

For non-relativistic mechanics, the formula above gives:

It sometimes is convenient to split the total kinetic energy of body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass rotational energy:

where:

For the translational kinetic energy of a body with constant mass m, whose center of mass is moving in a straight line with speed v, as seen above is equal to

where:

m is mass of the body v is speed of the centre of mass body

If a body is rotating, its rotational kinetic energy or angular kinetic energy is simply sum of kinetic energies of its moving parts, and thus is equal to:

where:

I is the body's moment of inertia ω is the body's angular velocity.

Thus kinetic energy is a relative measure and no object can be said to have a unique kinetic energy. But the total energy of the system, ie kinetic energy, fuel chemical energy, heat energy etc, will be conserved regardless of the choice of measurement frame.

The kinetic energy of an object is related to its momentum by the equation:

In relativistic mechanics

Einstein's relativistic mechanics must be used for calculating the kinetic energy of bodies whose speeds are a significant fraction of the speed of light:

Recall Einstein's famous formula:

E = mc2

For an object in motion:

,

where m0 is the rest mass, v is the object's speed, and c is the speed of light in vacuum.

So we approximate :

,

indicating that the total energy can be partitioned into the rest mass's energy plus the traditional newtonian energy (at low speeds).

For example, for a speed of 10 km/s the correction to the Newtonian kinetic energy is 0.07 J/kg (on a Newtonian kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 710 J/kg (on a Newtonian kinetic energy of 5 GJ/kg), etc.

For higher speeds, the formula for the relativistic kinetic energy is derived by simply subtracting out the rest mass energy:

.

The relation between kinetic energy and momentum is more complicated in this case, and is given by the equation:

.

What this suggests is that the formulae for energy and momentum are not special and axiomatic, but rather concepts which emerge from the equation of mass with energy and the principles of relativity.

In quantum mechanics

In quantum wave-mechanics, the expectation value of the electron kinetic energy, , for a system of electrons described by the wavefunction is a sum of 1-electron operator expectation values:

where me is the mass of the electron and is the Laplacian operator acting upon the coordinates of the i'th electron and the summation runs over all electrons. however, for the specific case of a 1-electron system, the kinetic energy can be written as

where T[ρ] is known as the Weizsacker kinetic energy functional.