Understanding conservation of angular momentum with examples

Question

I want to be sure I understand fully the conservation of angular momentum or/and the angular momentum itself with 3 examples, the first one I understand but the other 2 not really.

1. The famous giroscope precession with the biking wheel (Veritasium video), in the video, the reasoning used is that there is an angular momentum (red arrow) due to the spinning of the wheel and a torque (the finger pointing), and the precession is explained by saying the "Angular momentum follows the torque", which it's okay and I understand.

2. Bike and not falling. In this case, I was told by Brilliant app that the conservation of angular momentum is one of the causes that makes the biker to be harder to fall laterally, but then I try to draw the angular momentum due to the wheels' spinning (red arrow), and the external torque forced by a external force (gravity, green arrow) so it creates a torque (purple arrow) that points forward? Instead of pointing with the blue arrow so that it stabilised it?

3. Motocross bike jumping from one ramp to another ramp. In this different case, there is an angular momentum existing pointing outside of the image/phone, and then with the throttle, it would create an angular momentum that points inside of the image/phone, but how does conservation of angular momentum here also help to understand that it would allow for the rotation to be quicker?

Answer 1

About the case of the spinning wheel, as demonstrated in the video by Derek Muller (Veritasium).

About the narrative presented in the Veritasium video:
All that it does is to restate the observation in different words. There is no explanation there.

Let me describe an example of an actual explanation:
There is the phenomenon: when water freezes it increases in volume. If a water pipe is left filled with water when temperature goes below freezing the ice will burst the pipe.

The Wikipedia article that I linked to gives the explanation for that. The particular shape of the watermolecule, with the hydrogen atoms at a 107 degrees angle to each other, and the general properties of hydrogen bond forming, makes it favorable to form a hexagonal crystalline structure, resulting in ice taking up more volume than water.

The molecular explanation of the properties of ice takes the description to a deeper level.

By contrast: the following is not an explanation, but merely restating the observation in different words:
"Ice takes up more volume because the water-ice transition has a negative thermal expansion coefficient."

To avoid misunderstanding: the demand is not for exhaustive explanation When the explanation for ice is given the reader is asked to grant the properties of the water molecule, to grant the properties of hydrogen bridges. The thing is: the minimum to count as explanation is to go one level deeper. If the narrative merely restates the observation in different words then the narrative is conceptually still at the same level as the observation.

In the Veritasium video:
Derek points with his finger in the direction of the torque vector, and he observes: the direction of the precession follows the torque vector.

That is observation only, not explanation.

In another part of that video Derek describes a mathematical operation called 'vector cross product', and he observes: if you insert this vector and that vector into the formula for the vector cross product then the result is the observed precession.

Derek's attempt at explanation boils down to: "Gyroscopic precession occurs because the vector cross product says so."

However, it is an explanation when it answers the question:
Why do we find that the vector cross product of these two vectors describes the precession?

There is a 2012 answer by me in which an explanation for gyroscopic precession is given.

Answer 2

Your question 1 you said you understood by yourself.

Your question 3 is devoid of your own work and so it violates site rules.

I try to draw the angular momentum due to the wheels' spinning (red arrow)

This is correct

and the external torque forced by a external force (gravity, green arrow)

This is wrong. Weight is a force, it is not a torque. The green arrow is a force arrow. The yellow arrow is its idealised point of application away from the centre line joining the two wheel axes, which I take as the pivot of some sort.

so it creates a torque (purple arrow) that points forward?

This is wrong. Yellow cross green is the opposite direction of purple. Then you will get it correct.

Instead of pointing with the blue arrow so that it stabilised it?

This is not the correct direction.