Gyroscopic Precession in Layman's Terms

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I don't understand gyroscopic procession, you apply a force to a spinning wheel and the acceleration is applied 90 degrees further down or a torque is generated.

Imagine a wheel is spinning and you apply a force on the top of the wheel.

I try to imagine breaking down the parts of the wheel into infinitesimal masses and apply f=ma

I know that if you suppose the wheel would turn in the direction the force is applied, the mass on the axis not being accelerated will have a greater acceleration than the points on the wheel closer to the axis, and since the wheel is a fixed rigid disk the disparity in accleration will lead to some kind of normal force acting on the wheel.

and I figure that what must be going on is some normal force is applied behind the point at which you press on the wheel causing it to rotate.

I wonder then what would occur if you applied a torque yourself on the top of the wheel as its spinning.

If you spin the wheel slow or more quickly does it change how the wheel accelerates?

Does the axis of torque change according to the speed of the wheel? (assuming the place at which you apply force remains the same)

I seriously think it's easier just to study rigid-body mechanics and understand it for real than to bypass it by seeking explanations in "layman's terms".