Answer:
a) 2575 kgm²/s
b) 1.23 kJ
c) 0.478 rad/s
Explanation:
Given
Mass of astronauts, m = 74 kg
Length of rope, l = 8.53 m
Speed of orbit, v = 4.08 m/s
L = m1v1.x1(i) + m2v2.x2(i) = 2mv(d/2)
Thus, L = 2.m.v.(d/2)
L = 2 * 74 * 4.08 * (8.53/2)
L = 2 * 74 * 4.08 * 4.265
L = 2575.38 kgm²/s
Rotational Energy of the system
K(i) = 1/2m1v1(i)² + 1/2m2v2(i)²
K(i) = 2(1/2) * 74 * 4.08²
K(i) = 74 * 16.6464
K(i) = 1231.83 J = 1.23 kJ
Angular momentum is conserved, thus, angular velocity, w = v/r
w = 4.08 / 8.53
w = 0.478 rad/s
