Total work of pseudo forces in center of mass frame.
Show that total work done in center of mass frame on all the particles of a system by pseudo forces due to acceleration of mass center is zero.

Explanation

Let acceleration of mass centre relative to an inertial is `vec(a)_(c )`. Pseudo force on `I^th` particle of mass `m_i` in center of mass frame is `(-m_(i) vec(a)_(c ))`. Let displacement of Ith particle in a time interval is `Delta vec(r )_(i)` relative to the center of mass frame.
Total work of pseudo forces on all the particles in center of mass frame can now be expressed by the expression
`Sigma(-m_(i) vec(a)_(c )).Delta vec(r )_(i) = -vec(a)_(c).Sigma(m_iDelta vec(r )_(i))=-vec(a)_(c ).vec(0) = 0`