Why do gyroscopes not fall down?

[Aeronautic Freek]

he said torque is in direction into the board,but this torque don't have upward commoment so what keep gyroscope to not fall down because mg pull him down??so what is is force which oppose to gravity??
i understand that torque into the board cause gyroscope rotating in cricle(gyroscope precession) but what keep him to not fall down?

 

[Dale]

so what is is force which oppoese to gravity??

That is the upward force at the support. Without that force the gyroscope would fall like normal.

 

[Aeronautic Freek]

That is the upward force at the support. Without that force the gyroscope would fall like normal.

i don't understand ,can you show free body diagram of rotating gyro?
upward force at support exist even when gyro is not rotating but than gyro fall down..so rotaing gyro must produce some "new force" which act somewhere out of support if gyro is not falling.

 

[A.T.]

i don't understand ,can you show free body diagram of rotating gyro?

From: http://www.hyperphysics.de/hyperphysics/hbase/rotv2.html

upward force at support exist even when gyro is not rotating but than gyro fall down.

If it falls down then the froce is not the sameHere some good explanations of gyroscopic precession:

 

[Aeronautic Freek]

View attachment 265562

From: http://www.hyperphysics.de/hyperphysics/hbase/rotv2.html

i stil don't understand what keep gyro to not to flip down,(like do when is not rotating)...

 

[Dale]

upward force at support exist even when gyro is not rotating but than gyro fall down.. so rotaing gyro must produce some "new force" which act somewhere out of support if gyro is not falling

No new force, but the force at the support is less if it is falling than if it isn’t falling.

i stil don't understand what keep gyro to not to flip down,(like do when is not rotating)...

Can you clarify? Are you interested in why it doesn’t fall (linear motion) or are you interested in why it doesn’t flip (rotational motion)?

Up until this post you have been saying “fall” so I assumed you were interested in the linear motion and answered accordingly, but here you say “flip” so now I am unsure what you intend.

 

[Aeronautic Freek]

No new force, but the force at the support is less if it is falling than if it isn’t falling.

When i said "falling" i don't mean on faliing completely to the ground,i mean to flip/tilt(ROTATION MOTION) gyro down ,like gyro do every time when is not rotating...
(gyro can never fall down compltley because it is connected with rope ...i understand that..)

 

[Dale]

When i said "falling" i don't mean on faliing completely to the ground,i mean to flip/tilt gyro down ,like gyro do every time when is not rotating...
(gyro can never fall down compltley because it is connected with rope ...i understand that..)

OK, then you were using the wrong words. You want to ask about flipping or rotating not falling and you want to ask about torque not force.

The torque is horizontal so the angular momentum moves in the horizontal plane. To make it move down would require a downward torque. So the torque is in the wrong direction for it to flip down.

 

[Aeronautic Freek]

To make it move down would require a downward torque. So the torque is in the wrong direction for it to flip down.

gravity act at center of gyro mass, so downward torque = mg x L
how do you mean torque is in the wrong direction to flip it down?

 

[Leo Liu]

Check out this video, for Eugene Khutoryansky makes the most succinct physics animations.

First, you need to understand that the reason the wheel falls down when not rotating is because the torque creates a rotational motion of the wheel, centred at the end of the rope. If we don't want the wheel to fall, we need to find out a method to "consume" the torque. In this case, the rotation of the wheel does the job.

The gravity exerts a torque perpendicular to both the force vector and the arm which is the axle, on the wheel of the apparatus. Since we know that an external torque can change the angular momentum of the system, and the torque is perpendicular to the direction of the angular momentum, the torque simply changes direction of the angular momentum. As a result, the torque causes the wheel to rotate about the tip of the hanging rope and does not make the wheel fall down.

If you think my explanation is unintuitive, feel free to ask me to draw some diagrams for you.

 

[Aeronautic Freek]

Check out this video, for Eugene Khutoryansky makes the most succinct physics animations.

First, you need to understand that the reason the wheel falls down when not rotating is because the torque creates a rotational motion of the wheel, centred at the end of the rope. If we don't want the wheel to fall, we need to find out a method to "consume" the torque. In this case, the rotation of the wheel does the job.

The gravity exerts a torque perpendicular to both the force vector and the arm which is the axle, on the wheel of the apparatus. Since we know that an external torque can change the angular momentum of the system, and the torque is perpendicular to the direction of the angular momentum, the torque simply changes direction of the angular momentum. As a result, the torque causes the wheel to rotate about the tip of the hanging rope and does not make the wheel fall down.

If you think my explanation is unintuitive, feel free to ask me to draw some diagrams for you.

yes we must have some "righting moment" to counter dowanward torque caused by gravitiy(mgxL)
so yes you can draw some diagrams!

 

[A.T.]

i stil don't understand what keep gyro to not to flip down,(like do when is not rotating)...

Have you watched the videos? This question is asked once a month here, and has been explained many times.

 

[Dale]

gravity act at center of gyro mass, so downward torque = mg x L

No. The downward torque is 0. The $m \vec g \times \vec r$ torque is horizontal.

yes we must have some "righting moment" to counter dowanward torque caused by gravitiy(mgxL)
so yes you can draw some diagrams!

Gravity can never produce a downward torque. Gravity is vertical and torque is always perpendicular to the force. So a torque from gravity is always horizontal, never downward

 

[Aeronautic Freek]

No. The downward torque is 0. The mg→×r→ torque is horizontal.

yes obviusly net downward torque is zero,because gyro is not flip down,but this is non intuitive,maybe here starts all problems to me...
it is very strange to imagine where" righting moment" coming from, which counter gravity and make gyro to not flip down,,,,

 

[A.T.]

this torque don't have upward commoment so what keep gyroscope to not fall down

yes obviusly net downward torque is zero,because gyro is not flip down,

It seems that you don't understand the meaning of the torque vector direction.

 

[Dale]

yes obviusly net downward torque is zero,because gyro is not flip down,but this is non intuitive,maybe here starts all problems to me...
it is very strange to imagine where" righting moment" coming from, which counter gravity and make gyro to not flip down,,,,

You mention “net torque” and “righting moment” which makes me think you believe there are two torques involved. There is only one torque, the torque from gravity, and it points horizontally. There is no second torque to produce a net torque or a “righting moment” (whatever that is)

The torque is horizontal so the angular momentum moves horizontally.

 

[dRic2]

What we have so far proved is that if the wheel is precessing, it can balance the torque due to gravity or some other applied torque. But all we have shown is that this is a solution of an equation. That is, if the torque is given, and if we get the spinning started right, then the wheel will precess smoothly and uniformly. But we have not proved (and it is not true) that a uniform precession is the most general motion a spinning body can undergo as the result of a given torque. The general motion involves also a “wobbling” about the mean precession. This “wobbling” is called nutation.
Some people like to say that when one exerts a torque on a gyroscope, it turns and it precesses, and that the torque produces the precession. It is very strange that when one suddenly let's go of a gyroscope, it does not fall under the action of gravity, but moves sidewise instead! Why is it that the downward force of the gravity, which we know and feel, makes it go sidewise? All the formulas in the world like (20.15) are not going to tell us, because (20.15) is a special equation, valid only after the gyroscope is precessing nicely. What really happens, in detail, is the following. If we were to hold the axis absolutely fixed, so that it cannot precess in any manner (but the top is spinning) then there is no torque acting, not even a torque from gravity, because it is balanced by our fingers. But if we suddenly let go, then there will instantaneously be a torque from gravity. Anyone in his right mind would think that the top would fall, and that is what it starts to do, as can be seen if the top is not spinning too fast.
The gyro actually does fall, as we would expect. But as soon as it falls,...

You can read the full story here: https://www.feynmanlectures.caltech.edu/I_20.html#Ch20-S3

 

[Aeronautic Freek]

Gravity can never produce a downward torque. Gravity is vertical and torque is always perpendicular to the force. So a torque from gravity is always horizontal, never downward

why torque is allways prepedicular to the force?
so when gyro is not roatating,gravtiy is vertical and torque is prepedicular to gravity ,which mean torque is again horizontal?
why then gyro flip down if torque is horizontal even when gyro is not roatting?

 

[Leo Liu]

why torque is allways prepedicular to the force?

You are advised to read your textbooks. If you don't have one, I kindly suggest you to buy Serway's general physics textbook.

 

[Dale]

why torque is allways prepedicular to the force?

Because $\vec \tau = \vec r \times \vec F$. The cross product always gives an output vector which is perpendicular to both input vectors. That is how the cross product is defined.

so when gyro is not roatating,gravtiy is vertical and torque is prepedicular to gravity ,which mean torque is again horizontal?

Yes

why then gyro flip down if torque is horizontal even when gyro is not roatting?

Because in that case the gyroscope initially has 0 angular momentum. So increasing the angular momentum horizontally involves increasing the amount of spin about a horizontal axis, which is done by flipping down.

The difference is that in the spinning case the gyroscope starts with a very large angular momentum perpendicular to the torque. So instead of increasing the angular momentum it just turns it.

 

[vanhees71]

I strongly suggest to start learning about the vector product. It's essential to get the vector algebra really understood, before you can address classical mechanics. I'd say that the rigid-body dynamics is a subject that's on the higher-level end of a standard introductory (theoretical-)mechanics lecture. There's no way to have chance to understand it without being fluent in the only language physics can be properly expressed, which is math, and here it's vector algebra, including a detailed understanding of rotations!

I'd even recommend to teach it not without having Hamilton's principle at your disposal, because at least I could not understand it without this mathematical tool, which simplifies classical mechanics tremendously, but you can get far without the action principle too, as exemplified once more by Sommerfeld, Lectures on Theoretical Physics vol. 1 (of course, Sommerfeld was a real expert concerning rigid-body dynamics because he has written a very detailed work about it together with Felix Klein).

 

[etotheipi]

i stil don't understand what keep gyro to not to flip down,(like do when is not rotating)...
View attachment 265566

If you just attached it like that and let it go, without spinning it up first, the thing would just swing down like a normal pendulum. The torque due to gravity about the point where the axle meets the cord would still be horizontal, except it would just represent the change in the angular momentum vector per second, which would just get larger and larger in magnitude in one fixed direction on the down-swing.

Letting the wheel spin, e.g. in post #4, makes it slightly harder. The gravitational torque is still horizontal, except now we start off with the angular momentum vector pointing in the radial direction out from the wheel. Infinitesimally later the torque has caused this angular momentum vector to change direction, but it still lies in the horizontal plane and its magnitude is unchanged (it is similar to how the velocity vector changes during uniform circular motion).

We end up with precession, and you can write some equations of motion to make things more concrete. As @Dale noted, it is the upward tension from the cord that constrains the centre of mass to have zero vertical acceleration during precession.

 

[A.T.]

why torque is allways prepedicular to the force?

Definitions are chosen to simplify the math, and not necessarily to be intuitive. And if you don't find the definitions of torque and angular momentum vectors intuitive, then any explanation of the gyroscope based on these vectors will also not be intuitive to you.

An alternative is the explanation in the video below, which uses linear dynamics to explain it (e.g. force couple instead of torque):

 

[rcgldr]

1974 Laithwaite video, skipped to part starting with larger gyroscopes:

 

[A.T.]

1974 Laithwaite video, skipped to part starting with larger gyroscopes:

Laithwaites misconceptions are cleared up in the video below:

 

[Aeronautic Freek]

i find this explanation with linear analogy really good ,but it is still very unintutive why gyro don't flip down..

 

[A.T.]

i find this explanation with linear analogy really good ,

Yes, that's a nice one. Good find.

but it is still very unintutive why gyro don't flip down..

Yes it is, but you can always think of it as point masses with some linear momentum, which gets diverted.

 

[Dale]

it is still very unintutive why gyro don't flip down

Yes, it is definitely unintuitive. As you get further and further into physics things become less and less intuitive. You have to rely on the math more and more as you progress. Relativity and quantum mechanics are extreme examples, but as you see here even classical Newtonian physics can be unintuitive.

 

[Aeronautic Freek]

Yes, it is definitely unintuitive. As you get further and further into physics things become less and less intuitive. You have to rely on the math more and more as you progress. Relativity and quantum mechanics are extreme examples, but as you see here even classical Newtonian physics can be unintuitive.

If you must scale what will be hardiest branch of physics?
1)Clasiccal physics ;maybe fluid mechanics or thermodynamics?
2)in overall physics; general relativity or quntum physics?

"As you get further and further into physics things become less and less intuitive. You have to rely on the math more and more as you progress. "

yes that is beauty of math,cant never be wrong...but if scientist set wrong rules/equations when try to solve new phenomens in physics,results will be false even math is correct,so math doesn't mean nothing if things are not set correct..
interested how scientist set/discoverd new rules in phyiscs if something is not logic/intuitive!

 

[Dale]

yes that is beauty of math,cant never be wrong...but if scientist set wrong rules/equations when try to solve new phenomens in physics,results will be false even math is correct,so math doesn't mean nothing if things are not set correct.

Yes, this is definitely true. That is why we use experiments. We judge our math by how well it predicts experimental results. We even deliberately perform experiments where we think that our current equations might be wrong or where we have two different equations that disagree.

If you must scale what will be hardiest branch of physics?
1)Clasiccal physics ;maybe fluid mechanics or thermodynamics?
2)in overall physics; general relativity or quntum physics?

This is personal opinion, but I would definitely say fluid mechanics is more difficult than thermodynamics. But between GR and QM it is less clear to me. I think that GR is conceptually easier, but the equations are nonlinear so that is more difficult.