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?

1) 3,510 kg m²/s
2) 5,270 kg m²/s
3) 14,100 kg m²/s
4) 21,100 kg m²/s

Answer 1

The angular momentum of the person standing at 6.00 meters on the carousel is 3,510 kg m²/s.

Step-by-step explanation:

To calculate the angular momentum of the person standing at 6.00 meters from the center of the carousel, we can use the conservation of angular momentum. The formula for angular momentum is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since the angular momentum of the closer person is given as 2,340 kg m²/s, we can set up the equation:

L1 = L2

I1ω1 = I2ω2

The moment of inertia depends on the distance from the center of rotation, with larger distances resulting in larger moments of inertia. Since the first person is standing closer to the center (4.00 meters), their moment of inertia will be smaller than the second person who is standing further from the center (6.00 meters). Therefore, the angular velocity of the person standing at 6.00 meters will be smaller in order to balance out the equation and maintain the conservation of angular momentum. Thus, the angular momentum of the person standing at 6.00 meters is 1) 3,510 kg m²/s.