Why does the angular momentum always seem to follow the direction

[quietrain]

set up:

================ () (wheel)
|| (pivot) * take +ve y-axis directed to the right
* take +ve x-axis directed out of this screen
* take +ve z axis directed upwards

we know that weight of the wheel(-z-axis) about the pivot will produce a torque in the direction given by the right hand rule(into the screen).

if the wheel is spinning anti-clockwise, an angular momentum will direct to the +y-axis given by right hand rule.

so the torque will cause angular momentum to shift in the direction of "into the screen" .

so why does angular momentum follow the direction of the torque?

also, if right hand rule is just a convention, why does the angular momentum always seem to follow the direction of the torque in 1 way( into the screen) , instead of "out of the screen" since torque is just defined to be perpendicular to the force-radius plane?

i realize that the wheel always seem to precess in 1 direction about the pivot as a result...

anyone can solve my doubts?

thanks a lot!

 

[Franco_v]

The torque is equal to the rate of change of angular momentum (with respect to time). So if the torque acts into the screen, the "change" in the angular momentum vector (pointing in the +y-axis) must be into the screen as well. This means that the direction of rotation must be into the screen.

The right-hand rule is not a convention. It's a way to correctly visualize the direction of a vector or resultant vector when doing calculations. For example, if you were to calculate torque from the cross-product definition, the direction of the resultant torque vector would point in a certain direction (obviously). And you can determine the direction of this vector using the right-hand rule.

It turns out that in many calculations you can skip the more mathematically labourious cross-product calculation and just multiply length of moment arm by the force, with the direction given by the right hand rule.

 

[quietrain]

does it then mean that the wheel will always precess about the pivot in the counter clockwise direction? since the torque resulting from the weight of wheel about the pivot is acting into the screen ( given by right hand rule).

also, will the direction of the wheel spinning about its own axis affect the direction of precession about the pivot? meaning, if angular momentum points outwards in the +y-axis or pointing inwards towards the pivot in the -y-axis, will it have any effect on its rotation about the pivot?

or will it have any effect at all?

 

[Franco_v]

Yes, the wheel will always precess about the pivot, as long as it is spinning. So if there was a motor attached to it, it would precess forever.

If the wheel is spinning with spin vector in the +y-axis, the precession direction will be into the screen.

If the wheel is spinning in the opposite direction (with spin vector in the -y-axis), then the precession direction will be out of the screen (opposite direction). This is because the angular momentum vector is pointing in the opposite direction (towards the -y-axis), and the only way a "change" in this vector can point in the same direction as the torque (which is into the screen) is if the precession is in the opposite direction (out of the screen).

As a sidenote, the best way to understand precession (or any 3D motion) is to apply a full 3D dynamic analysis (e.g. Euler equations of motion for a rigid body). Introductory physics texts typically cut corners when teaching things like precession, and that's because it's inherently a three-dimensional problem, so they tend to "wing it", and the explanations tend to be somewhat incomplete/confusing as a result. So for a better explanation/understanding of what's going on it might be a good idea to just go straight to a full 3D analysis; then it's easier to understand the simplifications that are made in introductory physics texts when attempting to describe more advanced concepts like precession.

does it then mean that the wheel will always precess about the pivot in the counter clockwise direction? since the torque resulting from the weight of wheel about the pivot is acting into the screen ( given by right hand rule).

also, will the direction of the wheel spinning about its own axis affect the direction of precession about the pivot? meaning, if angular momentum points outwards in the +y-axis or pointing inwards towards the pivot in the -y-axis, will it have any effect on its rotation about the pivot?

or will it have any effect at all?

 

[quietrain]

i c... thank you very much

 

[Franco_v]

Correction, even if a motor turns the wheel, the wheel will only precess forever if there is no friction in the pivot and no air resistance. In a no friction environment there is no energy required to maintain the precession.

But if there is friction, then precession would take energy to overcome it, and this can only happen if the wheel were to lower in height; that is- give up some gravitational potential energy to provide the necessary energy to overcome the friction. There's more to it than this but from an energy perspective that's it in a nutshell.

I think I got it right this time :)