A satellite is spinning at 7.0 rev/s. The satellite consists of a main body in t

Question

A satellite is spinning at 7.0 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 4.0 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? (Enter the magnitude in kg · m2/s. Assume the main body of the satellite can be modeled as a solid sphere, even with the antennas projecting through it.)

Explanation / Answer

moment of inertia of the system is I = moment of inertia of solid sphere + moment of inertia of two rods

I = I1+ I2

I1 = (2/5)*m*R^2 = (2/5)*10000*2^2 = 16000 kg-m^2

I2=2*(1/3)*m1*L^2 = (2/3)*16*4^2 = 170.67 kg-m^2

I = 16000+170.67 = 16170.67kg-m^2

w = 7 rev/s = 7*2*3.142 rad/s = 43.988 rad/s

angular momentum is L = I*w = 16170.67*43.988 = 711315.44 kg-m^2/sec

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