A barbell consists of two small balls each with mass 400 gra

A barbell consists of two small balls, each with mass 400 grams (0.4 kg), at the ends of a very low mass rod of length d = 40 cm (0.4 m). The center of the barbell is mounted on the end of a low mass rigid rod of length b = 0.6 m (see Figure), and this rod rotates clockwise with angular speed 120 rad/s. In addition, the barbell rotates clockwise about its own center, with an angular speed 100 rad/s.

Solution

v = w * r = 120 * (0.4/2) = 24 m/s

L_trans = m v r = 0.4 kg * 24 m/s * 0.2 m = 1.92 kg·m²/s

L_tot = 1.92 kg·m²/s + 1.92 kg·m²/s = 3.84 kg·m²/s

I = 2 * m r² = 2 * 0.4 kg * (0.2 m)² = 0.032 kg·m²

L_rot = I * w = 0.032 kg·m² * 120 rad/s = 3.84 kg·m²/s