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 4300 kg and a radius of 2.1 m , 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 22 rpm in 3.5 min , starting from rest? Express your answer to two significant figures and include the appropriate units.

Answer 1

Given cylindrical satellite of  

mass M = 4300 kg , radius R = 2.1 m

rockcet of mass m = 250 kg ,

W = 22 rpm = 22*2pi/60 rad/s

dt = 3.5 min = 3.5*60 s

so the angular acceleration is alpha = dW/dt = (22*2*pi/60)/(3.5*60 )

alpha = 0.010971 rad/s2

now the moment of inertia of the system is  

I = M*R^2/2 + 4*m*R^2

because the four rockets are at the end of the sattelite at a distance of R from the center so

I = R^2 (M/2 + 4*m)

I = 2.1^2 (4300/2 + 4*250) kg m2

I = 13891.5 kg m^2

and the torque T = I*alpha and T = R*F sin theta here theta=90 degrees

so I*alpha = R*F ===> F = I*alpha/R

substituting the values

F = 13891.5 *0.010971/2.1 N

F = 72.573165 N

the steady force required of each rocket if the satellite is to reach 22 rpm in 3.5 min , starting from rest is

F = 72.57 N