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A satellite is spinning at 0.01 rev/s. The moment of inertia of the satellite about the spin axis is 2000 kg · m2. Paired thrusters are located at a distance of 1.5 m from the spin axis. They deliver their thrust in pulses, each thruster producing an impulse of 15 N ·s per pulse. At what rate will the satellite be spinning after 30 pulses?

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Answer:

Explanation:

Angular velocity of satellite

= 2π x .01

= .02 π rad /s

Initial angular momentum

Moment of inertia x angular velocity

= 2000 x .02 π

= 125.6 unit

Linear impulse produced by each thruster

= 15 N.s

Angular impulse

= 15 x 1.5 = 22.5 unit

Total angular impulse in 30 pulses

= 22.5 x 2 x 30

1350

This angular impulse will add total angular momentum of

1350 unit

So total angular momentum after 30 pulses

= 1350 + 22.5

= 1372.5 unit

So  final angular  velocity

= final  angular momentum / moment of inertia

= 1372.5 / 2000

=   0 .686 rad /s

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