This holds for a rotation around the center of mass. The moment of inertia around this axis can be then simplified to I = m 1 r 1 2 + m 2 r 2 2 = R 2 m 1 m 2 2 ( m 1 + m 2 ) 2 + R 2 m 1 2 m 2 ( m 1 + m 2 ) 2 = μ μ R 2 .