Kinetic energy
Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. The kinetic energy of a body is equal to the amount of work needed to establish its velocity and rotation, starting from rest.
Table of contents |
2 Heat as Kinetic Energy 3 See also |
Equations
Definition
In words the above equation states that the kinetic energy (E_{k}) is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal of the body's momentum (p).Newtonian Mechanics
where:- E_{k} is the total kinetic energy
- E_{t} is the translational kinetic energy
- E_{r} is the rotational kinetic energy
- E_{translation} is the translational kinetic energy
- m is mass of the body
- v is linear velocity of the centre of mass body
- ,
- E_{r} is the rotational energy or angular kinetic energy
- I is the body's moment of inertia
- ω is the body's angular velocity.
Relativistic Mechanics
In Einstein's relativistic mechanics, (used especially for near-light velocities) the kinetic energy of a body is:
- E_{k} is the kinetic energy of the body
- v is the velocity of the body
- m is its rest mass
- c is the speed of light in a vacuum.
- γmc^{2} is the total energy of the body
- mc^{2} is the rest mass energy.
Where gravity is weak, and objects move at much slower velocities than light (e.g. in everyday phenomena on Earth), Newton's formula is an excellent approximation of relativistic kinetic energy.
Heat as Kinetic Energy
Heat is a form of energy due to the total kinetic energy of molecules and atoms of matter. The relationship between heat, temperature and kinetic energy of atoms and molecules is the subject of statistical mechanics. Heat is more akin to work in that it represents a change in internal energy. The energy that heat represents specifically refers to the energy associated with the random translational motion of atoms and molecules in some identifiable matter within a system. The conservation of heat and work form the first law of thermodynamics.See also