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11 March, 20:35

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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  1. 11 March, 20:38
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    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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