# Change a Spacecraft's attitude from 3 - axis stabilised to spin stabilised?

I am essentially trying to "spin up" a s/c, so it spins about 1 axis at a known spin - rate. I then need to figure out how much time it will take to do that, and how much force required (which I imagine is a function of time). Am I correct in assuming the torque needed is M = Iw, where I is the moment of inertia of that axis, and w is the spin rate? From there, I am not sure how to calculate the time. Any help would be massively appreciated.

Best, Harvey

## 1 Answer

Your two questions "much time it will take to do that, and how much force required" are not independent!

This is a Second Law problem. Any amount of torque applied will spin the spacecraft. In your equation, w is not the spin rate, but the angular acceleration. The equation is analogous to F=ma for linear motion. You apply the amount of torque you want, to get the angular acceleration you need.

So if your spacecraft's initial spin rate is zero, and assuming a constant torque, the final spin rate is just wt - the angular acceleration resulting from the torque you apply, times the amount of time over which you apply it.