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PRACTICE / Angular momentum

Signed angular momentum survives internal friction

Two coaxial rotors have moments of inertia 3 kg·m² and 1 kg·m². Their angular velocities are +8 rad/s and −4 rad/s. An internal clutch locks them together.

What is their common final angular velocity?

Organize the givens & assumptions
  • I1 = 3 kg·m²; ω1 = +8 rad/s
  • I2 = 1 kg·m²; ω2 = −4 rad/s

Fixed common axis, negligible external torque impulse about that axis, constant inertias and eventual no-slip rotation. Clutch friction may dissipate kinetic energy.

  1. A5 rad/s5\ \mathrm{rad/s}
  2. B7 rad/s7\ \mathrm{rad/s}
  3. C2 rad/s2\ \mathrm{rad/s}
  4. D52 rad/s\sqrt{52}\ \mathrm{rad/s}

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