Correct explanation of how gyroscope works?

[hyunwoo126]

Homework Statement

Hi,

I'm taking AP Physics in high school, and the explanation I wrote is based on a demo in class, something like this picture:

When the wheel is spinning, there is an angular momentum facing away from the string along the axis of rotation of the wheel. The gravitational force creates torque, which points not downward but parallel to the floor and perpendicular to the rod. Torque, a cross product of radius and force, represents the rate of change in angular momentum over time—torque causes change in angular momentum. The rod-wheel system was slowly turning about the string because angular momentum was constantly turning towards the direction of the gravitational torque. The wheel cannot drop towards the floor because the gravitational torque only accounts for horizontal change in angular momentum of the wheel.

Is this explanation correct?
If there's anyway i can phrase better, please let me know.

 

[tiny-tim]

Welcome to PF!

Hi hyunwoo126! Welcome to PF!

The wheel cannot drop towards the floor because the gravitational torque only accounts for horizontal change in angular momentum of the wheel.

Nooo … the wheel can drop to the floor with horizontal angular momentum …

in fact, the only way it can not drop is if magnitude of the horizontal angular momentum is constant, isn't it?

(this isn't much different from the case of an ordinary circular pendulum … which will stay up even without spinning)

The important thing is to start with the rotational version of good ol' Newton's second law … torque = rate of change of angular momentum … using torque about the top of the string (it's the only point which you can be sure is stationary … remember, the string is not vertical ):

what conditions (of angle and speed) do there have to be for the magnitude of the horizontal angular momentum to be constant?

(btw, if you know how to use Euler's equations to calculate in a rotating frame you might try writing the equations both in a stationary frame and in a frame moving with the axle)

 

[hyunwoo126]

Thanks for the warm welcome and reply!

ughhh...this is so hard to grasp.

"The wheel cannot drop towards the floor because the gravitational torque only accounts for horizontal change in angular momentum of the wheel."

What I am trying to explain there is why the wheel resists dropping (ie tilting downward).

Nooo … the wheel can drop to the floor with horizontal angular momentum …

in fact, the only way it can not drop is if magnitude of the horizontal angular momentum is constant, isn't it?

so since the wheel is not dropping/tilting, the magnitude of horizontal angular momentum is constant...ok

However, the directional change in horizontal momentum (spinning of the rod-wheel about the string), is caused by the gravitational torque...right?

So what's keeping the wheel from dropping/tilting to the floor?
Is it because that would introduce a downward change in angular momentum, and conservation of angular momentum prevents that?
or
torque=rate of change in angular momentum, and since there is no torque downward, no change in angular momentum downward...

also, the wheel does tilt when the spinning of the wheel slow down...why...

thanks so much for your time.

 

[tiny-tim]

… What I am trying to explain there is why the wheel resists dropping (ie tilting downward).
…
So what's keeping the wheel from dropping/tilting to the floor?
…
also, the wheel does tilt when the spinning of the wheel slow down...why...

Hi hyunwoo126!

I suggest you think first about what would happen if the wheel were locked, and prevented from spinning …

so it would be a strange-shaped circular (or conical) pendulum …

(a bit like a "motorcycle wall of death")

even without spinning, it still won't drop, provided it's going at the "critical angle" for that speed (and below that angle, it will actually rise).

There's nothing special about spinning that keeps the wheel up …

the spinning simply changes the critical angle (for any particular speed) …

and less spinning means a "lower" angle.

 

[hyunwoo126]

"The gyroscope seems to defy gravity because the torque created by the spinning wheel counteracts the torque due to gravity. Gyroscopes have been used through history for varied uses such as stabilizing spacecraft or for guidance systems on ships and missiles."

I found this explanation on a youtube video description.


the spinning of the wheel produces torque? Isn't there has to be a force to have torque?

 

[tiny-tim]

the spinning of the wheel produces torque? Isn't there has to be a force to have torque?

Yes, you're right …

that youtube quote is rubbish! ​

tip: don't use youtube links … either use this forum, or use wikipedia

 

[hyunwoo126]

ehhh my head hurts...

so what is keeping up the wheel?
can you just tell me in straightforward...I really can't figure it out myself.

Thank you so much for your help btw.

 

[Shivanand]

Hi,

I too have similar doubts about gyroscopes. If you have already figured out the solution by yourself or by some other means could you please explain it to me?

Or if you have not, I would be glad if you can make sense out of the replies given to my question here
https://www.physicsforums.com/showthread.php?p=3458548".