4. The kinetic energy of a system of particles, whether they form a rigid body or not, can always be written as a sum of the kinetic energy of the center of mass of the system plus the kinetic energy of the particles' motion relative to the center of mass. Thus, if the system has mass M and the center of mass has speed V,

K = (M/2)V² + K_rel

where

K_rel = (m₁/2)v'₁² + (m₂/2)v'₂² + ...

and m₁, m₂, ... are the masses of the individual particles and v'₁, v'₂, ... are the speeds of the particles relative to the center of mass.

This result can be derived starting from Definition 2 of the kinetic energy of a system of particles.