A satellite in the shape of a solid sphere of mass 1,900 kg and radius 4.6 m is spinning about an axis through its center of mass. It has a rotation rate of 8.0 rev/s. Two antennas deploy in the plane of rotation extending from the center of mass of the satellite. Each antenna can be approximated as a rod of mass 150.0 kg and length 6.6 m. What is the new rotation rate of the satellite (in rev/s)

6.3 rev/s

Explanation:

The new rotation rate of the satellite can be found by conservation of the angular momentum (L):

The initial moment of inertia of the satellite (a solid sphere) is given by:

Where : is the satellite mass and r: is the satellite's radium

Now, the final moment of inertia is given by the satellite and the antennas (rod):

Where : is the antenna's mass and l: is the lenght of the antenna

So, the new rotation rate of the satellite is:

Therefore, the new rotation rate of the satellite is 6.3 rev/s.

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