Anything that spins has a momentum that was given to it by a force. People can spin a basketball on their finger, the energy is transfered from their arms and hands to put a spin on the ball. Once the ball is on their finger, it doesn't topple until the friction from their finger slows down the spin. So this ball somehow is able to balance itself while it is spinning, but what would happen if it wasn't spinning and you tried to balance it on your finger? (It would fall) Angular momentum, keeps it balanced because the energy given to it was for one direction. It would require more energy to change that direction, no matter how you do it.
If there was no friction (like in space) the basketball would just keep spinning until there was an equal and opposite force to overcome it's angular momentum.
If the ball is spinning on someone's finger, and they wanted it to suddenly spin the other way, they would have to apply quite a bit of force. It would probably sting a bit, because of the transfer of energy. It would take the same amount of energy to turn it upside down, because the results would be the same.
It took me awhile to learn this. Just remember that energy cannot be created nor destroyed. You can only transfer it. The energy you give something makes it go a certain direction, so that object will fight and resist any change to that initial direction. The only way you can change it, is if you provide the energy it requires.