The effect is called gyroscopic precession.

Here is a good demonstration video:

http://youtu.be/wt_nYn_XUvE

This is good too:

http://youtu.be/zbdrqpXb-fY

Thanks but am I still right?

JNB's reference to the bicycle wheel is a good suggestion. Take a front wheel from a ten-speed and hold it by the axle. Have someone spin it, and then turn the whole assembly this way or that using the axle. You'll immediately feel the gyroscopic effects.

Some children's museums or science museums have hands-on displays of gyroscopic effects using a spinning weight that you can manipulate.

Pick up a children's toy gyroscope and play with it a little. Spinning, the gyroscope is rigid in space, which is the property we use in mechanical gyro instruments (attitude). When the gyro is displaced, its motion is predictable, and it's that motion that's used to establish rate rate of turn. Gyroscopic effects are applicable to any spinning object, the most obvious of which is a propeller.

I'm not a physicist, so I won't attempt to explain the principle in that matter. When you pitch up, as in a climb, you are changing the PLANE OF ROTATION of the prop. Assuming the prop rpm is constant, the force applied will be shifted 90 degrees in the direction of prop rotation. That shift in force is felt as a left turning tendency. Get a bicycle wheel, spin it fast, then sit on an office swivel chair with your feet up and holding the wheel in front as a propeller. Move the wheel through different planes of motion. The chair will turn.

No, you sound mixed up. Let me try and sort this out.

Yep.

Not necessarily, unless someone told you to assume that for their particular teaching example. It's possible in the case of props and gyros as teaching tools, but actually not true in real life most of the time. Angular momentum is not always conserved in real life.

But let's back up a bit and start simple first. For now, we can assume the speed of a bicycle wheel or a prop is constant, and there is no friction or other acceleration acting on it.

Yes.

Not if it changes. But like I said, we can assume it is constant in the case of a bicycle wheel or prop disc for now as a learning assumption.

Not sure what you mean "make the prop rotate". Assuming we are using props as our example, here's how it goes.

1. A prop is fully spun up to begin with on a running engine. Turning at say 2400 rpm. This is constant speed, no change at any time for that.
2. A torque is applied in the form of a pitch input when the pilot raises the tail of the airplane using their stick. The torque is "seen" or felt on the prop disc at the top and the bottom. Actually it is applied though the engine drive shaft, but it does not matter how it is applied.
3. The airplane (prop disc etc.) responds with a left yaw. This is your gyroscopic precession.

Does this help?

You're reaching beyond where I think you should for now. I would not try and reach too far here by getting into conservation of momentum or anything that deep right now. All you need to know is how gyroscopic precession acts- a prop acts a like a big gyroscope and when it is already spun up to a normal running speed and torque is then applied to it via pitch input, it will react in another plane than the one in which the pitch torque is applied. Simple stuff- specifically, the plane of reaction is always 90 degrees to the upstream side on the disc or gyro where the original torque was applied. In this case the prop-gyro turns pitch torque into yaw torque. Are we ok now? I want to make sure we have that much before we get into it any deeper.

If you insist on going to a (verbal) mathematical level with this topic, see section 19.10.2. on the webpage below. He has a nice vector diagram showing how the various forces add up. Vectors offer an easy way to visualize spatial relationships involving force interactions.

*19**The Laws of Motion