Question

A 36.00 kg lead sphere is hanging from a hook by a thin wire 2.80 m long and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere.

a. The angular velocity of the lead sphere increases.
b. The angular velocity of the lead sphere decreases.
c. The angular velocity of the lead sphere remains unchanged.
d. The angular velocity of the lead sphere depends on the speed of the steel dart.

Answer 1

The angular velocity of the lead sphere will change due to the external impulse provided by the steel dart, as it adds to the system's angular momentum.

Step-by-step explanation:

The question you're asking is related to the conservation of angular momentum and the effect of external impacts on a rotating system's angular velocity. Conservation of angular momentum means that if no external torque acts on a system, the total angular momentum remains constant. When the steel dart strikes and embeds itself in the lead sphere, it introduces an external impulse, which changes the system's angular momentum. Therefore, the angular velocity of the lead sphere will change depending on the speed and direction of the dart at the moment of collision.