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 (Figure 1) . Suppose that the satellite has a mass of 2400kg and a radius of 4.3m , and that the rockets each add a mass of 250 kg.

What is the steady force required of each rocket if the satellite is to reach 31rpm in 6.5min , starting from rest?

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To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1) . Suppose that the satellite has a mass of 2400kg and a radius of 4.3m , and that the rockets each add a mass of 250 kg. What is the steady force required of each rocket if the satellite is to reach 31rpm in 6.5min , starting from rest?

Explanation / Answer

moment of inertia of system= 0.5*2400*4.3^2 +4*250*4.3^2 = 40678 Kg-m^2

w=alpha*t

==> (31*2*pi/60) = alpha*(6.5*60)

==> alpha= (31*2*pi/60)/(6.5*60) = 0.00832 rad/s^2

assuming Force =F

==> torque= I*alpha

==> 4*F*4.3= 40678*0.00832

==> F=19.6768 N

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