The Spinning Example With the Space Telescope

In the spinning example with the space telescope, I kind of it sort of feels like you did get away with something, right? Take you spun the mass one way and then you spun it the other way. And now you're in a different spot but your total orientation change direction. Well, part of the spaceship changes direction and another part changes direction in the opposite way. So the total angular momentum hasn't changed. But when you slow down to stop, you spin it the otherway and presumably, it's the same amount of momentum that you need to take out or put back in. Right.