Gyroscope - Conservation of Angular Momentum and Precession

I am having trouble understanding how a spinning gyroscope seemingly defies gravity.

What I got out of reading:

- L = Iw (kgm^2/s = kgm^2 x rad/s)
- mass is constant
- momentum: conserved
- therefore: if angular velocity stays the same, so will m
- object maintains its orientation
- as wheel spins slower, m gets larger

- gravity exerts downward force on gyroscope
- causes a torque that is perpendicular which makes the gyro precess

Please confirm if these points are correct.

What I don't understand is: if momentum is conserved, how does torque figure into it? How are torque and angular momentum related?

Keep in mind I'm only in high school, learning this on my own for a final project, so please try to keep it as simple as possible (no complicated math please!)

Thank you!

It is tricky, but I'll try. If you've done some Physics you'll know that F = ma = the rate of change of momentum, where linear momentum is just mass * velocity. This is just another way of saying that to change your momentum (slow you down or speed you up) there must be a force (push or a pull). When you go into rotational motion the force that makes things rotate is replaced by the torque (twist) of the force. Think of a wrench. The torque is the force multiplied by the distance from the nut or bolt. Mass is replaced by something called the moment of inertia (think of it as a resistance to a wheel speeding up or slowing down rotationally) Some wheels are easy to spin (small moment) and some are hard (large moment). The acceleration is replaced by an angular acceleration. So just like F = ma = rate of change of momentum, torque = moment of inertia times angular acceleration = rate of change of angular momentum. In a gyroscope, the torque is provided by the weight of the gyroscope trying to tip it over. But the torque is in a very special direction. It is actually horizontal. And since there is a torque, there must be a change in angular momentum, which is also horizontal. The only way that can happen is if the gyroscope rotates its angular momentum without changing its speed. So it moves in a horizontal circle without changing its speed. It's the direction that changes. It's a bit like circular motion. There is a change in velocity and so an acceleration and so a force without a change is speed. It's the direction that changes because velocity is a vector, so the arrow can keep the same length but change direction to accelerate. Angular momentum is also a vector.
I'm sure wikipedia describes it better than I can. Pictures help.