Question

Does the addition of mass to the outside of an already rotating mass add angular momentum?

1) Yes, it always adds angular momentum
2) No, it never adds angular momentum
3) It depends on the direction of rotation
4) It depends on the mass and distance of the added mass

Answer 1

The addition of mass can affect the system's angular momentum depending on the mass and its distance from the rotation axis, provided no external torque is applied.

Step-by-step explanation:

The addition of mass to an already rotating object may or may not add angular momentum to the system. When you add mass to a rotating object, you also affect the moment of inertia, based on the mass times the square of the perpendicular distance from the rotation axis (I = mr²). According to the law of conservation of angular momentum, if no external torque is applied, the system's angular momentum remains constant. This means that if you add mass in such a way that it does not apply any external torque, the system's angular momentum is conserved but its angular velocity will adjust to maintain the angular momentum, since L = Iω where ω is the angular velocity.

Therefore, the correct answer to the student's question is 4) It depends on the mass and distance of the added mass. The mass's contribution to the system's moment of inertia and the resulting system's angular velocity are what determine the final angular momentum of the system.