Central Forces 2023 (3 years)
(Messy algebra) Purpose: Convince yourself that the expressions for kinetic energy in original and center of mass coordinates are equivalent. The same for angular momentum.
Consider a system of two particles of mass \(m_1\) and \(m_2\).

Show that the total kinetic energy of the system is the same as that of two
“fictitious” particles: one of mass \(M=m_1+m_2\) moving with the velocity of the
center of mass and one of mass \(\mu\) (the reduced mass) moving with the
velocity of the relative position.

Show that the total angular momentum of the system can similarly be decomposed
into the angular momenta of these two fictitious particles.