Calculate the angular momentum, about the Earth's center, of an 84.3-kg person on the equator of the rotating Earth.

To calculate the angular momentum of an 84.3 kg person about the Earth's center, we use the formula for angular momentum:

L = m * v * r

where:
L = angular momentum (kg·m²/s)
m = mass of the person (kg)
v = linear velocity at the equator (m/s)
r = radius of the Earth (m)

Step 1: Identify Given Data
Mass of the person, m = 84.3 kg

Radius of the Earth, r = 6.37 × 10⁶ m

Angular velocity of the Earth, ω = 2π / T (where T = 24 hours = 86400 seconds)

ω = (2π) / (86400 s)
ω ≈ 7.27 × 10⁻⁵ rad/s

Linear velocity at the equator, v = r * ω

v = (6.37 × 10⁶ m) * (7.27 × 10⁻⁵ rad/s)
v ≈ 463.8 m/s

Step 2: Calculate Angular Momentum
L = m * v * r

L = (84.3 kg) * (463.8 m/s) * (6.37 × 10⁶ m)

L ≈ 2.49 × 10¹⁵ kg·m²/s

Final Answer:
The angular momentum of the person about the Earth's center is approximately 2.49 × 10¹⁵ kg·m²/s.