Kinetic Energy (redirected from Translational kinetic energy)

kinetic energy: see energy.

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kinetic energy

Form of energy that an object has by reason of its motion. The kind of motion may be translation (motion along a path from one place to another), rotation about an axis, vibration, or any combination of motions. The total kinetic energy of a body or system is equal to the sum of the kinetic energies resulting from each type of motion. The kinetic energy of an object depends on its mass and velocity. For instance, the amount of kinetic energy KE of an object in translational motion is equal to one-half the product of its mass m and the square of its velocity v, or KE = ¹⁄₂mv², provided the speed is low relative to the speed of light. At higher speeds, relativity changes the relationship.

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kinetic energy

the energy of motion of a body, equal to the work it would do if it were brought to rest. The translational kinetic energy depends on motion through space, and for a rigid body of constant mass is equal to the product of half the mass times the square of the speed. The rotational kinetic energy depends on rotation about an axis, and for a body of constant moment of inertia is equal to the product of half the moment of inertia times the square of the angular velocity. In relativistic physics kinetic energy is equal to the product of the increase of mass caused by motion times the square of the speed of light. The SI unit is the joule but the electronvolt is often used in atomic physics.

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kinetic energy [kə′ned·ik ′en·ər·jē]

(mechanics)

The energy which a body possesses because of its motion; in classical mechanics, equal to one-half of the body's mass times the square of its speed.

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Kinetic Energy 

the energy of a mechanical system, which depends on the velocity of motion of its points. The kinetic energy T of a mass point is equal to one-half the product of the mass m of the point and the square of its velocity ν: T = ½ mν². The kinetic energy of the system is equal to the algebraic sum of the kinetic energies of all of its points: T = Σ½mν_k². The expression for the kinetic energy of the system may also be written in the form T = ½Mν_c² + T_c, where M is the total mass of the system, νc is the velocity of the center of mass, and T_c is the kinetic energy of the motion of the system about the center of mass. The kinetic energy of a rigid body in translational motion is calculated in the same way as the kinetic energy of a point with mass equal to the total mass of the body.

When the system is displaced from configuration (1) to configuration (2) the change in the system’s kinetic energy arises from the action of external and internal forces applied to it and is equal to the sum of the work A_k^e and A_kⁱ performed by the forces over the given displacement: T₂ — T₁ = Σ_kA_k^e + Σ_kA_kⁱ. This equation expresses the theorem of the change in kinetic energy, which is used in solving many problems in dynamics.

At velocities approaching the speed of light, the kinetic energy of a mass point is

where m_o is the rest mass of the point, c is the speed of light in vacuum (m_oc² is the energy of the point at rest). At low velocities (ν « c) the above equation is transformed into the usual ½mν² formula.

S. M. TARG