Torque and Rockets for Spinning Satellites

[ahello888a]

Homework Statement

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure. If the satellite has a mass of 3600 kg, a radius of 4.6 m, and the rockets each add a mass of 230 kg, what is the required steady force of each rocket if the satellite is to reach 33 rpm in 5.3 min, starting from rest?

Homework Equations

moment of inertia for point masses (rockets) and cylinder (satellite) and torque and rotational kinematics

The Attempt at a Solution

So i first convert 33 rpm to 3.455 rad/s and 5.3min to 318s. Next I use the equation $$\omega$$ = $$\alpha$$ t and solve for $$\alpha$$. I get 0.1086 rad/s/s. then for the moments of intertia, I get 0.5 * (mass of rocket) * (radius)^2. I also get 4 * (mass of satellite) * (radius)^2. I added those together to get the total moment of inertia which is 38402.64 kg*m^2. To get the torque I multiply the total moment of inertia and the angular acceleration I found earlier and get 625N then divide by 4 for each rocket and get 156N. The program says this answer is wrong, but I don't see where the fault lies.

 

[D H]

I don't see where the fault lies.

You are doing several things wrong here. First,

So i first convert 33 rpm to 3.455 rad/s and 5.3min to 318s. Next I use the equation $$\omega$$ = $$\alpha$$ t and solve for $$\alpha$$. I get 0.1086 rad/s/s.

It is a good idea to make a rough calculation in your head. Here you have 3.455 radians/second per 318 seconds, or roughly 3 radians/second per 300 second, so about 0.01 radians/sec². That's a factor of ten smaller than what you got.

Next,

then for the moments of intertia, I get 0.5 * (mass of rocket) * (radius)^2. I also get 4 * (mass of satellite) * (radius)^2. I added those together to get the total moment of inertia which is 38402.64 kg*m^2.

Where did you get these equations? You didn't use the correct moment of inertia for a either a point mass or a cylinder.

Finally,

To get the torque I multiply the total moment of inertia and the angular acceleration I found earlier and get 625N

That is not a force! Moment of inertia has units of mass*length², angular acceleration has units of 1/time², so the product has units of mass*length²/time². Force, on the other hand, has units of mass*length/time². Moment of inertia times angular acceleration yields torque. What is the relation between force and torque?

 

[ahello888a]

First: I meant to type 0.01086 sorry for the typing error
Second: ahh made another mistake i meant...0.5 * (mass of satellite) * (radius)^2 and 4 * (mass of rocket) * (radius)^2
Third: so since force = torque/radius then i would be getting 625/(radius)/4 which comes out to 34N?

 

[D H]

That's it!

 

[ahello888a]

thanks very much!