Question

A satellite is spinning at 6.2 rev/s. The satellite consists of a main body in the shape of a solid sphere of radius 2.0 m and mass 10,000 kg and two antennas projecting out from the center of mass of the main body that can be approximated with rods of length 3.0 m each and mass 16 kg. The antennas lie in the plane of rotation. What is the angular momentum of the satellite about its center?

Answer 1

Answer:

$627031 kgm^2/s$

Explanation:

First convert angular speed from 6.2 rev/s to rad/s knowing that each revolution is 2π rad:

$\omega = 6.2 * 2\pi = 38.96 rad/s$

The we can calculate the moments of inertia of the satellite by summing up the 2 moments of inertia of the solid sphere and the 2 rods at their ends:

$I = I_s + 2I_r$

$I = \frac{2}{5}MR^2 + 2\frac{1}{3}mL^2$

$I = \frac{2}{5}10000*2^2 + 2\frac{1}{3}16*3^2$

$I = 16000 + 96 = 16096 kgm^2$

Then the angular momentum is the product of angular velocity and moment of inertia

$\omega I = 38.96 * 16096 = 627031 kgm^2/s$