To get a flat, uniform cylindrical satellite spinning at the correct rate, engin

Question

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure.

Part A

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure. Part A If the satellite has a mass of 3200kg , a radius of 4.9m , and the rockets each add a mass of 220kg , what is the required steady force of each rocket if the satellite is to reach 30rpm in 5.2min , starting from rest?

Explanation / Answer

here ,

Moment of inertia of this system ,I = I satellite + 4 * Irocket

I = 0.5 MsR^2 + 4 *Mr * R^2

I = 0.5 * 3200 * 4.9 ^2 + 4 * 220 * 4.9^2

I = 59544.8 Kg.m^2

the moment of inertia is 59544.8 Kg.m^2

Here ,

wf = 30 rpm = 3.141 rad/s

NOw , using first law of motion ,

wf = wi + a*t

3.141 = a * 5.2 * 60

a = 0.010067 rad/s^2

Using second law of motion ,

4 *F*4.9 = 0.010067 * 59544.8

F = 30.58 N

the required steady force of each rocket if the satellite is to reach 30rpm in 5.2min , starting from rest is 30.58 N

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