Examining the Physics of a Gyroscopic Softball

[Pocketwatch]

A softball sized ball is filled with hundreds of spinning micro gyroscopes.

The axis of the spinning gyroscopes are all pointing in random directions.

Will the ball resist being thrown and go shorter distances?

Will the ball resist rolling?

OR

Will it just behave like a normal ball being thrown, etc?

 

[pervect]

It depends - are the gyroscopes free to move (in which case they must rub against each other, presumably with friction), or is the whole assembly rigidly welded together?

 

[ZapperZ]

I vote for "it just behave like a normal ball being thrown".

Why? A collection of randomly orientated moment will produce a net moment of zero. For each one that points up, there has to be one that points down, etc. Case in point, a paramagnet. Each atom has a net magnetic dipole moment, but at room temperature, for example, they are all oriented randomly, resulting in no magnetic moment. So it just behaves like any old clump of stuff.

Zz.

 

[Danger]

A collection of randomly orientated moment will produce a net moment of zero.

But wouldn't each one resists movement in one plane? Intuitively, it would seem that a rigid assemblage of them would resist in all planes. You could still throw it like a regular ball, but could you make it spin?

 

[quasi426]

I think that compared with a ball of equal mass that does not have moving parts the ball with the mini gyros will have travel less. This is because the gyros will rotate and thus have rotational kinetic energy. This energy will therefore drain some of the translational kinetic energy and the ball should travel a smaller distance.

 

[ZapperZ]

But wouldn't each one resists movement in one plane? Intuitively, it would seem that a rigid assemblage of them would resist in all planes. You could still throw it like a regular ball, but could you make it spin?

But for each one resisting something in one plane, there's another "anti-resisting" it.

Say you have an object with two spinning wheels on top of each other. So this is like a gyroscope but with the axis of rotation along a single line. The top gyroscope spins in one direction, the bottom gyroscope spins in the opposite direction. What is the net moment? Zero. You might as well not have any gyroscope. They are coupled as such.

I saw on TV a while back on a huge helicopter that has two sets spinning blades on opposite sides of a "wing".. one spins one way, the other spins the other way. As a result, the helicopter does not need a tail stabilizer because its net moment is zero just from the two spinning blades alone.

Zz.

 

[pallidin]

A softball sized ball is filled with hundreds of spinning micro gyroscopes.

The axis of the spinning gyroscopes are all pointing in random directions.

Will the ball resist being thrown and go shorter distances?

Will the ball resist rolling?

OR

Will it just behave like a normal ball being thrown, etc?

What an interesting question!
My 2-cent's worth: If the ball was thrown without rotation there should be no effect, as the axis of the multiple mini-gyros would not change orientation.
However, if thrown WITH an imparted or encountered rotational influence, certainly there would be a "resistance" to such rotation(depending on the gyro-arrangements, of course)

 

[Pocketwatch]

Thank you for your informative answers.

The alignment of the axis of the tiny gyroscopes would affect what happened to the ball when it is thrown.

If all the spinning axis were arranged a certain way in the ball, the ball would tend to break apart if it is thrown hard enough.

If all the spinning gyroscopes were properly arranged the ball would hold together better and go farther when thrown.

If we are using ungimbaled gyroscopes, what would probably be the best arrangement of the spinning axis to give the ball maximum velocity when thrown?

 

[Q_Goest]

Regarding the OP, I would agree with Danger though I won't claim any expertise in gyroscopes. I think the commentary by Zz is incorrect because it presumes a gyroscope can create a moment. If it creates a moment then without any other moment resisting it, the gyroscope can't be in static equilibrium and must be in dynamic equilibrium which means its axis must not only rotate about some point, the gyroscope as a whole will have an angular acceleration and must accelerate around that point.

My understanding is a gyroscope can only resist a moment, it does not create one. I think the analogy to atoms and molecules may be inappropriate as I don't think there's any "anti-resistance" going on. Here's a few quotes:

At high speeds, the gyroscope exhibits extraordinary stability of balance and maintains the direction of the high speed rotation axis of its central rotor. The implication of the conservation of angular momentum is that the angular momentum of the rotor maintains not only its magnitude, but also its direction in space in the absence of external torque.

Ref: Hyperphysics

The fundamental equation describing the behaviour of the gyroscope is:
t=Ia

Ref: Wikipedia
where t= torque
I = moment of inertia
a = angular acceleration

From what I gather from these two references, a gyroscope can only resist a moment or torque about its axis. Simply being able to resist a moment doesn't seem to explain precession though. There's a good explanation of how precession works at "How Stuff Works" which basically says:

Newton's first law of motion states that a body in motion continues to move at a constant speed along a straight line unless acted upon by an unbalanced force. So the top point on the gyroscope is acted on by the force applied to the axle and begins to move toward the left. It continues trying to move leftward because of Newton's first law of motion, but the gyro's spinning rotates it, like this:

(See picture at "How Stuff Works")

The same article also says:

If you mount two gyroscopes with their axles at right angles to one another on a platform, and place the platform inside a set of gimbals, the platform will remain completely rigid as the gimbals rotate in any way they please.

Ref: How Stuff Works
For any two gyroscopes that are at right angles inside this ball of mini gyroscopes, any two gyroscopes resist rotation in all directions. If the ball has all these pairs of gyroscopes inside resisting rotation in all directions, it would seem the ball would only have additional resistance to motion in all directions, not some anti-resistance because there are more than one set of orthoganal gyroscopes.

 

[pervect]

The previous post by O_Goest was quite well documented, but unfortunately is quite wrong.

The commentary about two gyroscopes mounted at right angles is not relevant to the problem, the point that needs to be understood is what happens when two gyroscopes are rigidly coupled together and oriented in opposite directions (180 degree angles), i.e. if you have a gyroscope whose spin axis via the right hand rule is pointing "up", and another one whose spin axis is pointing down.

There are a couple of ways of understanding this. One way is to look at the precession of the pair of gyroscopes, and show that they are equal and opposite.

http://www.gyroscopes.org/behaviour.asp

takes this approach. It points out that for a car carying a gyroscpe in a particular orientation, turning to the right will force the nose of the car down. It also mentions that if the gyroscope were spinning in the opposite direction, the nose of the car would be forced up instead. Combining these two effects, one achieves the result that there would be no net force on the turning car with a pair of identical gyroscopes spining in opposite directions.

This is verified by practical examples, such as the helicopter with counter-rotating blades that was previously mentioned.

There is an easier approach. The wikipedia, mentioned by the previous poster, gives the fundamental equation

http://en.wikipedia.org/wiki/Gyroscope

torque = dL/dt

where L is the angular momentum of the gyroscope.

The total angular momentum, L, of a pair of counter-rotating gyroscopes is zero. Thus a system with a pair of counter-rotating gyroscopes rigidly joined together will act just like a system with no gyroscope.

Note that the joining must be rigid. Large forces can be generated in the process of attempting to change the orientation of a such a pair of gyroscopes quickly, which could break the joining if it were not strong enough.

 

[Q_Goest]

pervect, thanks for the comments. Again, I want to emphasize I have no expertise in this, but it's a curious question. Perhaps you can help clarify a few things.

First, if we consider translational motion, including acceleration of this ball in any linear direction, I think we all agree there's no affect from the gyroscopes. What I'm confused on is strictly the rotational acceleration.

To clarify this discussion, let's define a coordinate system as is used conventionally, with the X axis being horizontal, Y vertical, Z into/out of the page. Now we put identical gyroscopes on a common axle at X1 and X-1 rotating in opposite directions on the X axis. If we put a moment on this pair of gyroscopes which is around the Z axis, one thing that happens is each gyroscope wants to precess in opposite directions. That is, they put a moment on the axle around the Y axis in opposite directions. These moments are equal and opposite, so they cancel. Is that correct?

Now if I'm not mistaken, they also both put a moment around the Z axis, but I'm not sure that one is equal and opposite. Isn't there a moment created around the Z axis? Isn't that moment equal and in the same direction?

The commentary about two gyroscopes mounted at right angles is not relevant to the problem

I have to disagree here. I'm sure you will agree that no matter what way one examines any given problem, you must come to the same conclusion. If there is no affect from the gyroscopes, then there must be some reason why this way of looking at it is either incorrect or perhaps, gives you the same answer. For example: Perhaps by suggesting that 2 gyroscopes at right angles are not symetrical so you need a total of 6 to make it symetrical (ie: at the following points on our coordinate system: X1, X-1, Y1, Y-1, Z1, Z-1).

One final thought, this question would seem to be applicable to atoms in a metal matrix, is that correct? Perhaps you could comment, especially regarding angular momentum in atoms. Do atoms behave like miniture gyroscopes?

 

[ZapperZ]

Regarding the OP, I would agree with Danger though I won't claim any expertise in gyroscopes. I think the commentary by Zz is incorrect because it presumes a gyroscope can create a moment. If it creates a moment then without any other moment resisting it, the gyroscope can't be in static equilibrium and must be in dynamic equilibrium which means its axis must not only rotate about some point, the gyroscope as a whole will have an angular acceleration and must accelerate around that point.

I don't think you understand what a "moment" is.

If something has a moment of inertia (and I'd like to see you argue that a gyroscope doesn't have one especially when you have to apply a torque to make it spin), then it has a "moment" (angular momentum) when it is spinning. That is what makes it want to conserve its angular momentum in the first place.

Zz.

 

[Creator]

If all the spinning gyroscopes were properly arranged the ball would hold together better and go farther when thrown.

What arrangement and where is your reference for this, if I may ask?

This implies rotational momentum is being converted to linear motion without external interaction. Moreover, if it can "go farther" when thrown, then you've just figured a way to reduced its inertial mass.
Don't tell NASA until I can get my gyroscope production facility up and running.

Creator

 

[Q_Goest]

Zz, regarding a moment. In mechanical engineering, a moment is a torque or a rotational force around a point. A wheel such as a gyroscope is made from has a moment of inertia which is a bit different from the moment of inertia* which resists bending as described in the stress analysis of a beam, but yes, I understand moments.

Zz said: A collection of randomly orientated moment will produce a net moment of zero.

If something has a moment of inertia (and I'd like to see you argue that a gyroscope doesn't have one especially when you have to apply a torque to make it spin), then it has a "moment" (angular momentum) when it is spinning.

I realize now you meant that each gyroscope has angular momentum, with each gyroscope having its angular momentum in a different direction, hence the term "moment" meaning each gyroscope has angular momentum in a given direction. My mistake, I thought you were suggesting each gyroscope actually was creating a moment meaning a torque. My apologies for miss quoting you.

Perhaps you could help explain if the description I gave is true/false and why.

To clarify this discussion, let's define a coordinate system as is used conventionally, with the X axis being horizontal, Y vertical, Z into/out of the page. Now we put identical gyroscopes on a common axle at X=1 and X=-1 rotating in opposite directions on the X axis. If we put a moment (torque) on this pair of gyroscopes which is around the Z axis, one thing that happens is each gyroscope wants to precess in opposite directions. That is, they put a moment (torque) on the axle around the Y axis in opposite directions. These moments (torque) are equal and opposite, so they cancel. Is that correct?

Now if I'm not mistaken, they also both put a moment (torque) around the Z axis (I should say they resist the torque applied to the Z axis), but I'm not sure that one is equal and opposite. Isn't there a moment (torque) created around the Z axis?

I've modified my comment slightly as I see it can also be misinterpreted.

Just one more clarification regarding moment or torque that may help. If we have a bicycle wheel (gyroscope) suspended from a string from one end of the axle, the wheel wants to fall down, but instead it precesses around the string. In order to support the wheel, there must be a moment around the point where the string and axle meet which is equal to the distance from that point to the CG of the wheel times the weight of the wheel, otherwise it would fall. It's this torque which is exerted by gravity in this case, or by acceleration in the vertical direction which causes the gyroscope to precess. Also, the rate of precession is a function of it's angular momentum (what you've been calling "moment").

Anyway, again I appologize for miss quoting you!

* Inertia is another one of those terms which has multiple meanings. Granted, they are analogous ones, but different.

 

[pervect]

pervect, thanks for the comments. Again, I want to emphasize I have no expertise in this, but it's a curious question. Perhaps you can help clarify a few things.

First, if we consider translational motion, including acceleration of this ball in any linear direction, I think we all agree there's no affect from the gyroscopes. What I'm confused on is strictly the rotational acceleration.

To clarify this discussion, let's define a coordinate system as is used conventionally, with the X axis being horizontal, Y vertical, Z into/out of the page. Now we put identical gyroscopes on a common axle at X1 and X-1 rotating in opposite directions on the X axis. If we put a moment on this pair of gyroscopes which is around the Z axis, one thing that happens is each gyroscope wants to precess in opposite directions. That is, they put a moment on the axle around the Y axis in opposite directions. These moments are equal and opposite, so they cancel. Is that correct?

I assume you mean you are applying a torque around the z, axis, i.e. by pushing "down" on the leftmost gyroscope and pushing "up" on the rightmost gyroscope.

Now if I'm not mistaken, they also both put a moment around the Z axis, but I'm not sure that one is equal and opposite. Isn't there a moment created around the Z axis? Isn't that moment equal and in the same direction?

I think you are confused here. Consider representing angular momentum as a vector. I assume you know how to do this?

The rightmost gyroscope, rotating around the x axis, will have an angular momentum vector that points along the x axis. For definiteness, say that it points to the right. The leftmost gyroscope, rotating around the x axis, then has an angular momentum vector that points to the left.

Now, when we apply a torque to rotate the assembly around the z axis, the system rotates just the same when the gryos are spinning as when they are not.

We can see that the spin of the gyroscopes has no effect, because the angular momentum vectors of the two gyroscpes cancel each other out, so the angular momentum of the entire system, whichis the sum of the angular momentum of all its parts. is not affected by whether or not the gyroscopes are spinning

The angular acceleration of the assembly is thus equal to the moment of inertia of the system around the z axis divided by the torque, independntly of whether or not the gyroscpes are spinning or not.

However, there will be large stresses on the joining rod. These stresses are due to the fact that we must apply a large torque represented as a vector in the 'y' direction on the rightmost gyroscope, and a counterbalancing torque represented by a vector in the 'minus-y' direction on the leftmost gyroscope, in order to shift their axes of rotation. We can see this by drawing the state of the system after it has rotated along the z axis.

Note that the total torque is zero. However, because the two torques are applied at different postions along the rod, there is quite a bit of stress on the rod that joins the two gyroscpes. The faster the system rotates around the z axis, the larger the stress gets. The greater the angular momentum stored in the gyroscoples, the larger the stress gets. I haven't worked out what happens when the bar starts to bend, but as long as it is rigid, there are no oppositional torques generated, so a small torque along the z axis will cause the angular velocity about the z axis to accelerate, meaning that the stress will increase linearly with the amount of time the torque is applied.

 

[Pocketwatch]

Thanks again for your answers.

I keep thinking that there is a connection between an object in motion and

gyroscopic action. Both resist course changes.

An object at rest and a gyroscope tends to resist movement.

Is it possible that resistance to being put in motion, vector changes and resistance to being stopped are all just gyroscopic action within matter?

 

[pervect]

Thanks again for your answers.

I keep thinking that there is a connection between an object in motion and

gyroscopic action. Both resist course changes.

An object at rest and a gyroscope tends to resist movement.

Is it possible that resistance to being put in motion, vector changes and resistance to being stopped are all just gyroscopic action within matter?

The short answer is no - gyroscopic action comes from inertia - inertia does not come from gyroscopic action.

 

[Pocketwatch]

That is the whole point of my question!

What causes inertia?

I know that nobody knows!

I am trying to figure it out.

 

[Pocketwatch]

I may have to resort back to my theory that the resistance to acceleration is due to time dilation.

Acceleration causes a physical change in matter that slows relative time.