Kinetic Energy

Kinetic energy represents the energy associated with the motion of an object. It is defined as:

K ≡ mv² / 2 for a point mass and <math> K = {1 \over 2}mV^2 + {1 \over 2} I \omega ^2 </math> for a rigid body, where I is the body's moment of inertia and omega is the body's angular velocity.

The change of kinetic energy is equal to the total work done on it by the resultant of all forces acting on it. For a point mass this can be expressed as:

ΣW = ΔK = mv_f² / 2 - mv_i² / 2

Where v_i is speed at t = 0 and v_f is speed at time = t.

Kinetic energy is a scalar and has the same units as work (i.e. Joule).

Note that if the mass of an object is increased, the increase in kinetic energy increases linearly; if the velocity of an object is increased, the increase in kinetic energy increases quadratically. For example, doubling the mass of an object doubles its kinetic energy; doubling its velocity quadruples its kinetic energy.

Kinetic Energy in Relativity

The energy of a particle in relativity is:

<math> E = \gamma m_0 c^2 </math>

where <math>\gamma</math> is the Lorentz factor, <math>m_0</math> is the rest mass and c is the speed of light.

Since this includes the mass energy of the particle, we must subtract a factor of <math> m_0 c^2 </math> to get the energy due to the particle's motion, the kinetic energy, as:

<math> K = (\gamma - 1) m_0 c^2 </math>