Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass
Show K = K + 1/2 `MV^2`, where k is the total kinetic energy of the system of particles, K is the total kinetic energy of the system when the particle velcoities are taken with respect to the centre of mass and `MV^2//2` is the kinetic energy of the translation of the system as a whole (i,e of the centre of mass motion of the system).

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vecp = vec p_i + m_i vecV where vecp_i is the momentum of the ith particle

Define centre of mass of a system of particles.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :- Show (dL')/(dt)=(sumr_i') xx (dp')/(dt) Further, show that (dL')/(dt)= tau'_(ext) where tau'_(ext) is the sum of all external torques acting on the system about the centre of mass.

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.