Pure Translation

 

Translation of a system of particles

 

Newton's second law for a single particle

 

∑F = ma

 

Newton's second law for a system of particles

 

A system made up of several particles may be analyzed as a whole or as a set of individual particles. If the system is analyzed as a whole, the acceleration term in Newton's second law is of the overall center of mass (a_G). If the system is analyzed as individual particles, then the ma terms for all of the particles are summed.

 

∑F = ma_G     or     ∑F = ∑m_ia_i

 

Note that internal reaction forces sum to zero and do not need to be included in Newton's second law.