Why does a gyroscope resist rotating towards the ground?

[FIphysics]

Today in class we have an intro to gyroscopes where my professor gave the classic "bicycle wheel" example where he spun a bicycle wheel to give it significant angular velocity, attached one end of the wheel apparatus to a string fixed to the ceiling, and let the wheel hang and precess (just like as shown in this video ). I understand how the angular momentum is in the -x direction (typically cartesian 3-d system) and the torque due to the gravitational force is in the +z direction, but I cannot rectify this with why the wheel resists rotated towards the ground. Can anyone help me to understand this?

 

[Dr Lots-o'watts]

Watching that video was almost a spiritual experience.

Not sure I follow your coordinate system, but if you paint a red dot on the tire representing an atom, it sure wants to go in a straight line as much as it can. The spokes keep it in a circular motion, but gravity doesn't have much of a say in this until the red dot has lost momentum to friction.

 

[Cleonis]

I cannot rectify this with why the wheel resists rotated towards the ground.

The first image shows a gimbal mounted gyroscope wheel. From outside to inside there is a yellow housing and a red housing. (I will get to the green arrows - and another detail - later.)

I will define three axes:
# Roll axis - the gyroscope wheel spins around the roll axis.

# Pitch axis - motion of the red housing, as you can see, the gimbal mounting ensures the pitch axis is perpendicular to the roll axis.

# Swivel axis - motion of the yellow housing.


First start the gyroscope wheel spinning fast. Then add some swivel.
The second image shows a single quadrant.

Rather than trying to mentally follow the entire wheel as it spins I suggest you divide in four quadrants, and you consider the mechanics of the motion in each quadrant.

I will concentrate on the quadrant of the second image now.

The mass in that quadrant is moving towards the swivel axis. Think of a point particle somewhere along the wheel rim, for example the point where the green arrow starts. That point is circumnavigating the swivel axis, with a corresponding velocity. Moving closer to the swivel axis the point has a tendency to pull ahead of the overall rotation. (Compare what happens when you twirl around an object tied to a string. Pull on the string to make it shorter and the object goes around faster.)

Repeating the first image:

(The brown cilinder represents a weight that tends to pitch the gyroscope wheel.)

In two of the quadrants the wheel mass is moving towards the swivel axis, in the other two away from the swivel axis.

The green arrows represent precession-caused tendency for each quadrant. Combining the four quadrants you see there is a pitching effect.

You can apply that finding to the example of the bicycle wheel demonstration. When the bicycle wheel is precessing there is a state of dynamic equilibrium. Gravity imparts a tendency to pitch down, the precessing motion imparts a tendency to pitch up. Those two tendencies are in dynamic equilibrium.

Full story, including math, is in the http://www.cleonis.nl/physics/phys256/gyroscope_physics.php" article on my website.

 

[pallidin]

Funny how my fast spinning car tires don't prevent me from flipping over in a bad turn.
OK, that's just humor...

 

[PJC01]

The resistance to rotating towards the ground in a gyroscope is due to the principles of angular momentum and torque. When the bicycle wheel is spinning and attached to a string, it has a significant angular momentum in the -x direction. This means that the wheel wants to continue spinning in the same direction and resist any changes in its orientation.

At the same time, the gravitational force is exerting a torque in the +z direction. This torque is trying to change the orientation of the wheel and make it rotate towards the ground. However, the angular momentum of the wheel resists this change and causes the wheel to precess, or rotate around a different axis, instead of rotating towards the ground.

This can be understood by considering the conservation of angular momentum. In order for the wheel to rotate towards the ground, its angular momentum would need to change. However, according to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the external torque from the gravitational force is not enough to overcome the wheel's significant angular momentum, so it precesses instead of rotating towards the ground.

In summary, the resistance to rotating towards the ground in a gyroscope is due to the principles of angular momentum and torque. The wheel's significant angular momentum resists any changes in its orientation, while the external torque from gravity is not strong enough to overcome this resistance. This results in the wheel precessing instead of rotating towards the ground.