# Torque Force of Rockets On A Satellite

1. Nov 15, 2009

### Lancelot59

1. The problem statement, all variables and given/known data

A satellite has a mass of 4000 kg, a radius of 4.9 m. 4 rockets tangentially mounted each add a mass of 220 kg, what is the required steady force of each rocket if the satellite is to reach 31 rpm in 5.1 min, starting from rest?

2. Relevant equations

$$\Sigma$$T=I $$\alpha$$

3. The attempt at a solution

Simple enough. I had already solved pretty much the same problem in my textbook.

I got $$\alpha$$ by taking the RPM as the delta Vtangental and then multiplying it by 2$$\Pi$$/60, and then dividing it by 306 seconds.

Then for I I used (1/2)Mr2 for the satellite body, and treated the rockets as point particles using mr2, and multiplying by 4.

I = (1/2)Mr2 + 4(mr2)

I wound up with about 183 newtons per rocket, which the program says is wrong. This online system has a habit of telling you your stuff is wrong when in fact you're doing everything correctly. It uses some silly method of rounding off each step instead of just the final answer.

Am I doing something wrong?

2. Nov 16, 2009

### tiny-tim

Hi Lancelot59!

(have an alpha: α and an omega: ω and a sigma: ∑ and a pi: π )
erm why 2π/60 ?

v = rω

3. Nov 16, 2009

### Lancelot59

Well the speed is in rotations per minute. So I changed it into radians per second.

31RPM x (2pi radians/1 rpm) x (1 minute/60 seconds)

I tried using v=r$$\omega$$ which gave me twice the $$\alpha$$ but the thing still says it's wrong. I calculated the moment of inertia to be 69148.8.

4. Nov 16, 2009

### tiny-tim

ah, I got confused by your Vtangential (still am, actually)!

Your equations, and moment of inertia, look ok, except I don't understand where you're using v =rω.

I have a feeling that your attempt to introduce V is somehow spoiling he result.

5. Nov 16, 2009

### Lancelot59

Well then how could I find alpha?