PLEASE HELP! To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four [Solved]

For the sake of time I will just use the numbers and information that I was assigned. (Same problem)
m_sat 3600kg
m_rocket 250kg (x4)
r 4m
T 5min=300s (capital T = time)
32 rpm

F= t/4r
F=500.416/(4*4m)
F=31.276N = 31N

Ftot = Q/R = 6817 N

ALMOST DONE
Now remember that the torque is the force applied times the radius (t=rF). Well, we already know t and r so lets solve for F. It is important to remember that our force is split evenly between four rockets.

Ftot = Q/R = 6817 N

4. Lets find torque
t=(44800N*m)(.01117rad/s^2)
t=500.416N*m

ALMOST DONE
Now remember that the torque is the force applied times the radius (t=rF). Well, we already know t and r so lets solve for F. It is important to remember that our force is split evenly between four rockets.

For the sake of time I will just use the numbers and information that I was assigned. (Same problem)
m_sat 3600kg
m_rocket 250kg (x4)
r 4m
T 5min=300s (capital T = time)
32 rpm

1. Find w (omega)
32rev/min x 2pi/rev x 1min/60s = 3.351 rad/s

2. Find a (alpha)
a=w/T
a=(3.351rad/s / 300s)
a= 0.1117s

3. Remember that we are looking for torque overall (t=Ia), to find this seeing as how we have a already we need to find I.
***THERE ARE TWO TYPES OF INTERIA ACTING***
It is easy to think that seeing as how it is a solid cylinder that you can simply add the mass of the rockets to the satellite and use .5(Mr^2) for your answer. This is ONLY correct for the satellite!!! (visualize the rockets in rotation) They would make a ring around the satellite. Therefore the interia of the rockets will follow Mr^2.

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Therefore your calculation should add the two interias acting.
I= (.5(3600kg)4m^2) (1000kg*4m^2)
I=44800N*m

4. Lets find torque
t=(44800N*m)(.01117rad/s^2)
t=500.416N*m

ALMOST DONE
Now remember that the torque is the force applied times the radius (t=rF). Well, we already know t and r so lets solve for F. It is important to remember that our force is split evenly between four rockets.

F= t/4r
F=500.416/(4*4m)
F=31.276N = 31N

This post is last updated on hrtanswers.com at Date : 1st of September – 2022