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)

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

Explanation:

The expression for conservation of the angular momentum (L) is

Where

initial moment of inertia and angular velocity

is the final moment of inertia and angular velocity

The expression of moment of inertia of the satellite (a solid sphere) is

Where is the satellite mass

r is the  radus of the sphere

Substititute 1900kg for m and 4.6m for r

The final moment of inertia of the satellite about the centre of mass

Where is the antenna's mass and

I is the length of the antenna

So, the Final rotation rate of the satellite is:

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

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