Navigation Links
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.

Contents

Equations

Definition

the words in the above equation state that the kinetic energy (Ek) 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

For non-relativistic mechanics, the total kinetic energy of a body can be considered as the sum of the body's translational kinetic energy and its rotational energy, or angular kinetic energy:

where:

Ek is the total kinetic energy
Et is the translational kinetic energy
Er is the rotational kinetic energy

For the translational kinetic energy of a body with mass m, whose centre of mass is moving in a straight line with linear velocity v, we can use the Newtonian approximation:

Etranslation is the translational kinetic energy
m is mass of the body
v is linear velocity of the centre of mass body

Thus, for a speed of 10 m/s the kinetic energy is 50 J/kg, for a speed of 100 m/s it is 5 kJ/kg, etc.

If a body is rotating, its rotational kinetic energy or angular kinetic energy is calculated from:

,

where:

Er 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:

where:

Ek 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.
γmc2 is the total energy of the body
mc2 is the rest mass energy (90 petajoule/kg)

It is an edifying exercise to show that the ratio of this relativistic kinetic energy to the Newtonian kinetic energy given by (1/2)mv2 approaches 1 as v approaches 0, i.e.,

This can be done by the techniques of first-year calculus.

Relativity theory states that the kinetic energy of an object grows towards infinity as its velocity approaches the speed of light, and thus that it is impossible to accelerate an object to this boundary.

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.

The next term in the approximation is 0.375 mv4/c², e.g. for a speed of 10 km/s this is 0.04 J/kg, for a speed of 100 km/s it is 40 J/kg, etc.

The exact Taylor series is

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 mechanical work form the first law of thermodynamics.

See Boltzmann constant and heat capacity.

See also


'"/>


(Date:9/17/2014)... have obtained the first partial genome sequence of an ... at the site of the Montsoriu Castle in Girona, ... closely related to today,s Iberian pig. Researchers also discard ... Iberian pigs. , The study, published in Heredity ... species, and particularly on that of the Iberian breed, ...
(Date:9/17/2014)... September 17, 2014 Researchers at UTSouthwestern Medical ... the circulating protein apolipoprotein E, called apoE3, helps repair ... called apoE4, do not get the benefit of this ... , "We believe that we have identified one mechanism ... why a genetic variant, apoE4, is detrimental," said ...
(Date:9/17/2014)... 1960s. The typical development phases of trees and stands ... as much as 70 percent. This was the outcome ... Universitt Mnchen based on long-term data from experimental forest ... findings were published recently in Nature Communications . ... topic, with the very survival of large forest ecosystems ...
Breaking Biology News(10 mins):Iberian pig genome remains unchanged after 5 centuries 2Protein variant may boost cardiovascular risk by hindering blood vessel repair 2Global change: Trees continue to grow at a faster rate 2Global change: Trees continue to grow at a faster rate 3
... is available in German . , ... , is able to rapidly ,and efficiently detoxify chemical ... the Tokyo subway attacks in 1995. A detailed understanding ... is ,necessary for efforts aiming to improve their properties. ...
... of Canada,s southern Rockies are a more distinct breed ... by University of Calgary researchers that is shedding light ... In a study published in the current issue of ... Design PhD candidate Byron Weckworth and his research group ...
... release is available in French . ... is pleased to announce that Concordia,s Centre for Structural ... research done by nine universities which are part of ... focusing on the conversion of agricultural waste into biofuel ...
Cached Biology News:Structure of enzyme against chemical warfare agents determined 2Mountain caribou's ancient ancestry revealed 2
Other biology definitionOther Tags