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


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.

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