Why doesn't a spinning wheel flop down when suspended by its axle?

[Alkatran]

We had a demonstration in physics, which I'm sure most of you have seen, of a wheel spinning very quickly maintaing it's orientation. (There is a string hooked to one end of the axle, and you expect the wheel to 'flop' downwards)

Now, I was just wondering what the math behind this is?

The spinning wheel has a high angular momentum in direction X while there is a torque from gravity in direction Y: after that...? This is definitely similar to it being difficult to slow an airplane rather than a ball.

 

[NateTG]

We had a demonstration in physics, which I'm sure most of you have seen, of a wheel spinning very quickly maintaing it's orientation. (There is a string hooked to one end of the axle, and you expect the wheel to 'flop' downwards)

Now, I was just wondering what the math behind this is?

The spinning wheel has a high angular momentum in direction X while there is a torque from gravity in direction Y: after that...?

The spinning wheel is typically called a gyroscope, and the movement is referred to as precession.

I'm pretty sure that it's possible to work things out starting from linear momentum to see that there's a net torque on the wheel as a rigid object by, for example, looking at the necessary change in velocity of point masses along various places on the gyroscope to tilt the axle while the wheel remains spinning.

 

[bionic_atom]

F=force
m=mass
0=theta
I want to say F=mdcos0 but I am not 100% sure, and in physics when we are not 100% sure we say were just guessing.