Classical Mechanics - Special Interest Problem

Show that the total kinetic energy of two masses orbiting one another may be express as

1/2m1v12 + 1/2m2v22 = 1/2mv2

where

m = m1m2 / (m1 + m2)

v = vr2 + r2w2

Note that both masses orbit about the common center of mass at distances r1 and r2 respectively, such that

r = r1 + r2

m1r1 = m2r2.

Note also that w is the same for both particles.

Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.