Question

Two people, each with a mass of 65.0 kg, are on the same carousel. One is standing 4.00 meters from the center, and the other is standing 6.00 meters from the center. If the closer person has an angular momentum of 2,340 kg m²/s, what is the angular momentum of the person standing at 6.00 meters?

a) 3,510 kg m²/s
b) 5,270 kg m²/s
c) 14,100 kg m²/s
d) 21,100 kg m²/s

Answer 1

The angular momentum of the second person on the carousel, standing 6.00 meters from the center, is calculated using conservation of angular momentum to be 3,510 kg·m²/s.

Step-by-step explanation:

The question involves calculating the angular momentum of a person on a carousel based on another person's known angular momentum at a different radius. In rotational systems, angular momentum (L) is conserved when no external torques act on the system. Thus, if we assume that the carousel is an isolated system, we can set up the following relation based on conservation of angular momentum:

L1 / r1 = L2 / r2

Where L1 is the angular momentum of the first person (2340 kg·m²/s), r1 is their radius from the center (4.00 m), L2 is the angular momentum of the second person at radius r2 (6.00 m). By solving for L2, we get:

L2 = (L1 × r2) / r1

L2 = (2340 kg·m²/s × 6.00 m) / 4.00 m

L2 = 3510 kg·m²/s

Thus, the angular momentum of the person standing at 6.00 meters from the center is 3,510 kg·m²/s, which corresponds to option (a).