Fly on a football problem.

Velocity of the fly relative to what?

If you say 'relative to the ball' then it is self evidently the fly's walking speed (say F)

Well if it's relative to some arbitary fixed axis then it's the velocity of the ball (say B) added to F (vector addition...

Now since B can be virtually anything between +/- V due to the Fly's meanderings then the resultant can also be just about anything between +/- 2V ????

Maybe I've oversimplified and got the maths a bit wrong..you'll have to wait for FYZ maybe... but I don'r reckon I'm far off.

Del

I think somebody is looking for excuses for England loosing in the Rugby World Cup. It is called a fly half and not a fly.

The fact is that the fly would not move / turn the ball all by walking in any direction. Can a child on a merry go round reduce the speed by pulling on the reigns of the wooden horse? or get it to move faster by whipping the wooden horse?

The turning inertia of the ball do not depend on gravity.w

I suggest some 44gal drum walking before an answer.

Some time ago there were a TV add about the power steering of a German car that is so light too steer that a mouse walking on top of the steering wheel will turn the wheel.

What I am looking for is a general expression for instantaneous velocity of the fly.

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Hi Mr. Collins,

The velocity of the fly with respect to what? Let's (just for a moment) imagine the fly is driving a tiny little car. I'm guessing your question is not what the car's speedometer would read, yes? If not, then you will need to specify the coordinate system in which the velocity measurement has meaning.

If the fly abruptly changes direction at the end of each leg of its journey, the 'function' you're looking for will be discontinuous. I'm assuming the fly changes direction in this manner, yes?

We're talking about a European-style football here (spherical), not an American-style football?

Looking forward to hearing from you!

-e

As the fly makes it's first step and goes to a walking pace(for a fly) he imparts an impulse to the spherical ball. From then on he does not accelerate and merely carries on walking and does not add any further impulse to the ball. the adhesion of his feet will have to be pulled off = a slowing aspect, but he will add a little energy to maintain his walk = cancels out. And change will add a new vetor, and so on. Since a football weighs 425 grams and a fly weighs about 10 milligrams and we assume 97% of the mass of the football is within 1 cm of the skin it has 42,500 times the mass of the fly, so the fly will not spin it much.

It's a really really big fly.

You know that, and I know that, but Mr. Collins needs to specify his coordinate system. One poster, below, says the system is with respect to the fixed stars, but Mr. Collins didn't actually say. Nor did he say which kind of football he's talking about. If an American-style football, we'll need a mathematical description of it. This is a relatively easy problem to solve, but I will defer its solution pending more rigorous information from Mr. Collins. As Abe Lincoln said, "If I have eight hours to cut down a tree, I'll spend six of them sharpening my axe." (or something like that). I don't want to waste time solving the wrong problem.

It sound a silly puzzle --Yes it does!!!-- but it has a serious purpose. I am extremely curious what possible "Serious Purpose" could there be. An explanation or definition of your purpose might enhance the quality of the responses you recieve.

This is kind of like the question --- How much does a fly slow your 65 MPH car upon impact with the windshield, and what is the difference if it is headon or you hit the fly from behind. GIMMEE A BREAK

Internet gambling. Flies playing soccer in orbit, like offshore gambling no jurisdictional problems

Nice reply LMAO

OK, look at the diagram above. It doesn't matter Werther the ball is in a gravitational field or not. If the fly first walks around the center of the ball (assuming it's possible), the fly adds angular momentum to the ball, causing it to spin like a bullet.

Next, if the fly walks end-to-end, his walk will have to overcome the angular momentum produced by his first walk. If he does, the ball will tumble end-over-end as it proceeds through space.

Finally, if the fly was to walk around the ball describing a flat plane that intersects the ball, he now has to overcome two angular momentums - the x and the y. If he can do this, he will put a tumble on the ball in the XY direction.

In one sense, you can say that the fly's first walk provided XZ rotation, the second walk provide YZ rotation, and the third walk provides XY rotation. I don't think you can get a lone Z motion on the ball, because that would involve the fly either raising or lowering the ball in its trajectory.

So ignoring the fly's acceleration as it starts walking, the fly's motion is linear. Therefore, THE FLY'S instantaneous rate of change is a constant number, which is equal to its walking velocity, and keep in mind that during each walk he had to expend more energy to counteract the angular momentum of the ball.

So what the hell is this for, anyway?!

The team must have lost and it is the dang fly's fault-- they should have sprayed for flies before the game and the outcome would have been different.

No! While the fly can impart spin on the ball, he cannot affect its trajectory. So if the receiver is in the zone, he'll still catch the ball, crush the fly, and run it in for 6 points!

Ahhh I see -- the fly is in serious danger no matter what he/she does and the game goes on.

It doesn't matter Werther the ball is in a gravitational field or not. If the fly first walks around the center of the ball (assuming it's possible), the fly adds angular momentum to the ball, causing it to spin like a bullet.

So that means if all of man kind went out side and at the same time we walked in the same direction we could increase or decrease the rotation speed of the earth on it's axis. I now have an answer for those who say "not enough hours in a day". We now can make more.

I am not sure I can develop an expression for the path of the fly, but I think many readers are misunderstanding your question. So first off, it is a spere, not an oval. Secondly, it this sphere is not going anywhere. It is in a gravity free condition. It is just hanging there. Wind velocity is ignored; assume the fly is really a point which we move on the surface of the sphere. So all of this boils down to simply a coordinate system upon the surface of a sphere, and the point is moved here and there, and Bob Collins wants a mathematical expression for the motion of the point. Now it does not matter one bit whether this point has feet that cause the more massive sphere to rotate in the opposite direction... oh wait, yes it does, because if the point gets the sphere moving in angular direction, then supposedly, that angular motion will be maintained through simple angular momentum, and then if the point decides to move in a different direction, that original angular motion will have to be vectored in with the new motion/direction of the point. OK, just discussing here. As I said, I could not really come up with the math, but I am hoping to better nail down the problem. What do you said Mr. Bob? --jer

I was wondering what a fly would look like with a space suite and how it will suck itself to the surface in the absence of air.

A fly should be called a Sit or a Walk because that is when it is a nuisance.

This is apparently a NASA trained fly. (years and $ in training) so it will be experimenting in the inside of a pressurised space module and will be able to move / spin the ball.

1st it has jump up from its perch (moving the space module slightly)

The fly towards the ball (switching off lift component of flight) (it might only reach the ball by chance)

Land with a thump on the ball - and have it move in that direction

The way a fly walks need to be defined. I haven't inspected it yet but I think it sucks itself too the surface and swings one leg at a time.

The forces working on the ball would then only be produced by the swing of a tiny leg.

Movement will be only noticed by the fly and should be ignored. It will in any case not live to tell.

Bob - I assume you're talking about an ideal situation here, no friction losses, no wind etc, but in the real Universe.

My take on it is this. As you say, when the fly starts to walk the ball rotates (much slower) in opposite direction. With ref to some postings, velocity is relative to the "fixed stars" (Newton would have said relative to absolute space, but it doesn't affect this discussion). If the fly stops, the ball stops. I conclude from that that if the fly changes direction, the components of velocity of fly and ball in the original direction become zero, leaving only the new ones. So the fly is always walking in its latest direction, the ball rotating opposite.

Anybody comment?

Also not sure what you mean by "a general expression for instantaneous velocity of the fly". As I see it, the fly's movements would be an input to the problem, not a result.

Don't know whether above is any help.....Codey

Exactly right. It doesn't matter if the fly stops and starts in a new direction or changes direction by walking round a slight curve: the overall result is as if the fly stopped (and the ball stopped) and the fly started again in the new direction. The total angular momentum of the whole system remains zero.

Does it? Think about it...

If the fly stops, the ball stops. I conclude from that that if the fly changes direction, the components of velocity of fly and ball in the original direction become zero, leaving only the new ones. So the fly is always walking in its latest direction, the ball rotating opposite.

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Please illustrate.

Hello Europium, I can't agree with that. It's true that if the fly stops, the fly contributes at that instant a negative impulse in the direction of travel only, but the ball contributes a positive impulse in the same direction. The 2 impulses cancel, the angular momentum being zero before the fly started walking, after he started and after he stopped.

If he doesn't stop but changes direction, I believe the argument applies to the components of momentum in the original direction.

Codey

Please illustrate, using a two-leg trajectory at the outset. Two terminal conditions:

1) The fly continues walking after the first change of direction.

2) The fly stops after the first change of direction.

Compute the magnitude of the net angular momentum (only) for each terminal condition. Note that the fly's location on the ball is irrelevant for the purposes of this computation.

Hello Codey,

Please also note (some haven't) that the original poster specified that the fly changes direction only. The OP did not say that the fly stops before changing direction. If the fly stops before changing direction, then of course the momentum vectors will sum to zero, provided the fly stops at the end of the last leg. But the OP never says the fly stops before changing direction, and so the picture will be very different. If we stop the fly before changing direction, we're changing the original problem statement.

-e

Assume it is a spherical football (as an American, I envisioned pointy ends which makes it a harder problem). Angular momentum is conserved. As the fly walks, it will give the ball angular momentum in one direction and itself exactly opposite angular momentum. Calculate the moment of inertia of the ball and the moment of enertia of the fly. The angular velocity of each will be inversely proportional to its moment of inertia.

First we need to specify the species of fly.

This problem cannot be solved because of the constrants of the question. First he states that the football is in a GRAVITY FREE CONDITIONS then he states

The fly then starts to walk around the ball causing the ball to rotate about an axis in the opposite direction through the system's (ball plus fly) C of G .

Now, I we are in a gravity free condition, how can we have a C of G? It would not exist!

Next question, what fixes the fly as stationary? Otherwise the fly would move about the ball without being able to rotate the ball. In a gravity free condition, the difference would be split equally, ball would rotate at 1/2 speed of fly?

Center of Mass would be more appropriate here, yes.

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Otherwise the fly would move about the ball without being able to rotate the ball.

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Not so. The fly's sticky feet would keep it on the ball, and the fly is pushing against the ball when it accelerates. For every action there's a reaction (remember Newton's laws), and the ball would rotate in the opposite direction by a much smaller amount due to its and the fly's relative masses.

Replace the fly with an astronaut, and think of the astronaut walking on the free-floating (much larger) ball by means of magnetic shoes. Would the ball - and astronaut - move? Heck yes they'll move, in opposite (tangential) directions.

Here is my 2¢

In this frictionless, gravity-free enviroment... The fly would make the ball rotate as it started to walk around it (conservation of angular momentum)

The 'sudden' changes in direction would impose a momentary stop of the fly. The stop would also stop the ball from rotating (conservation of angular momentum again). As this is a closed system, it's total angular momentum would always be at what it started - zero.

So hopefully with some simple force x distance equations, and a couple laws of Newton... your silly problem will have a real world solution

The 'sudden' changes in direction would impose a momentary stop of the fly.

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Why must the fly stop first, then turn?

I assume due to the distance between the fly's centre of gravity and the balls surface and the radius of the ball, and the fly walking at a constant speed, then the advance of the fly is a ratio between the balls radius and the fly's centre of gravity, to imply otherwise is to state that all the applied force gos into the ball and none into the fly? but the problem I wish to raise is, when he changes direction, without stopping, then one has to take into account the gyroscopic affect of the ball, so I think this fly will end up going round in circles? as it wobbles into its new axis.

Regards JD

Yep. This problem requires a stepwise solution of the momentum tensor.

Don't forget that after the fly starts its first excursion it has an equal and opposite angular momentum to the ball. And, therefore when it turns the corner there are equal and opposite gyroscopic effects in play. Otherwise: one way or another you're going to defy the law of conservation of angular momentum.

I know that this is a bit like saying that some over unity engine can't work because it defies the second law of thermodynamics, without, actually finding the flaw in the logic, but, starting with the answer should always help to confirm the "workings".

If the fly gallops, meaning he jumps forward using the ball as sort of a spring board and in the right direction, he may be able to impart the spin to the ball.

what if the fly hangs on and operates his wings? He can turn in any direction and apply the right torque to stop the spin, like a steering rocket?

Yes your right it wont wobble, the axis will act at 90 deg, to the applied force, and as such will have to be taken into account in a vector diagram. Direction plus correction. I think this is what you are saying, not fully at ease with the terminology.

Thank you all for your very valuable responses. Please keep them coming because they are helping me to understand my problem better.

As I am sure we would all agree it is very difficult to pose a question and include all the factors that contribute to a solution as well as all the simplifications that we might allow.

I did not state the problem very well. I tried to arouse interest by using a what I thought was an analogue of the problem I want to solve but of course in the process of so doing I introduced more ambiguity.

Let me have another go; the ball is spherical and I apologies for the first foolish mistake assuming that all footballs are round; I should have known better. Think of a billiard cue ball, (white, not that I think it matters) with a spot (black or what ever colour you like). There is no wind force acting on it and it has no translational velocity. I don't think that this last point matters because you might ask relative to what.

From a rectangular frame of reference with origin at the center of mass (thanks for that C of G observation) the ball rotates at a constant surface velocity about, lets say the X axis. At the same time it rotates about the Y and Z axes with the same surface velocity. I have kept the number of axes to three and equal velocities in order to simplify the problem.

What have I left out; oh yes, I sit at the origin of the system and I want an expression for the velocity of the spot.

I hope that this helps.

Hello Bob,

Perhaps we could define the coordinate system this way:

• It is with respect "to the fixed stars"

• The X-axis connects the fly, initially at rest on a non-moving ball, and the center of mass.

• The fly starts walking, imparting momentum to the sphere. Now the sphere has an axis of rotation perpendicular to the plane containing the first leg of the fly's trajectory. Define this as the Y-axis.

• Let the Z-axis be orthogonal to the X- and Y-axes.

• The center of mass is the coordinate-system origin.

Do you want the fly's velocity to be expressed as an angular velocity? This would be simpler, although if you want the fly's tangential velocity on the sphere you can easily convert between the two provided you know the sphere's radius (let's just call it R).

I'm assuming from your original post that the fly does not stop first when it changes direction, and that the change of direction is instantaneous. Is this the case?

Take care,
-e

Hello again, Bob,

As the sphere's radius is fixed, any point on the sphere can be described using two coordinates. Just thought I'd point that out.

Is the fly also spherical?

If so I may be able to derive a general case...

Sadly, the fly is shaped like an American football <sigh>

Not sure of my facts on this one, so others may shoot it down? when thinking of a rotating bodies about an axis "x", one would refer to the x axis as the actual, then if you apply a force "y" in some other direction then its axis is implied, the resultant is that the actual moves to occupy the position of the implied which is at 90deg to the applied force.(making sense?). If you add a further force "z", then the actual unable to occupy the position of either the implied "x" or "z" will move between them continually rotating, example north pole rotating down to the south pole infinitum. This of cause assumes that all force are equall, just one fly or is it two, darn I will have to get the pest man in.

Forget the fly for a minute: I think what Bob is really asking is how complicated can the equations of spin be (for an object with no external forces acting on it). We (UK and US) are all familiar with spinning balls, and, most sports balls tend to spin about a single axis whose direction (and sense) remains fixed. But, it is possible to spin a cricket ball so that it curves first one way then the other through the air and may "break" either way when it hits the ground. This is effectively extreme precession, a bit like the earth spinning around an axis through the North and South Poles, and, the North and South poles very slowly tumbling over each other. But can all "spin" be reduced to rotation about two axes, or do you need three. And how complicated could the equation of motion be of say New York relative to fixed coordinate axes with their origin at the centre of the earth.

The cricket ball reminds me of another post on quantum mechanics, do you think sub atomic particles have multiple axis of spin that makes there responses random? Sorry.

Regards JD.

Aaaaah: at those scales we may be dealing with more than three spacial dimensions so I suppose you might need more than three axes to fully describe the spin.

I like it. JD

Well, I admit I haven't read every post, but here's a real simple question (I hope)...

1. OK, a sphere moving through space in a straight line.
2. The sphere has a spin perpendicular to its linear motion, such that the sphere spins like a rifle bullet.
3. Therefore the sphere has a certain amount of stored angular momentum.
4. Some "force" acts on the sphere such that it tries to induce a second axis of spin, which is perpendicular to the first axis of spin - let's say the force tries to spin the ball parallel to the forward motion of the ball.
5. The force that tries to create the second spin axis will have to do work to overcome the angular momentum of the first spin.
6. As time progresses, won't the second spin ultimately cancel out the angular momentum of the first spin.
7. And by doing so, eventually stop the sphere from spinning in it's original axis -thus once again, the sphere is spinning about only one axis.

So the question is: without using external forces continually adding angular momentum to each of the sphere's spinning axes, one and only one axis of spin can exits (the one with the most energy) at a time?

The way I see it is, an object can have three different axis, First the actual axis where the mass is moving about its centre of gravity "x". Second an implied axis which act at 90deg to a additional applied force "y", Third an axis of transition where the masses realign them selves "z".

So a bullet is travelling trough space and spinning about its centre of gravity, it then encounters another force, this force has an implied axis "y" and a further axis of transition "z" is generated as the bullet move to its new axis, where it will continue to spin as it continues through space. The "x" axis position then becoming the "y" axis position.

But if a bullet encounters more than one force, you then have multiple implied axis, then the axis of transition "z" becomes dominant and the bullet will tumble end over end as it travels though space. still spinning on its axis, but if the implied forces are not equall then one might suppose the "x" axis may varry in its direction?

This is only my own thoughts on the matter and are not necessary correct.

Regards JD.

OK, but if the bullet is spinning, it is doing so on the original angular momentum that was imparted to it. This angular momentum is stored and there is only so much of it. There is no refreshing the supply. A force that wants to impart another axis of momentum to the bullet has got to overcome the spin (angular momentum) of the bullet each time it rotates on the new axis, which if strong enough to do so will ultimately dampen the bullets original angular momentum (or spin).

So, like if you take a gyroscope, and keep moving it such that you feel the force of its angular momentum, you will ultimately use up the original angular momentum and dampen its original spin to zero. Seems like it would anyway?

I can't answer the question directly but have come up with the following. The only circumstance I can think of where a constant force is applied, is a spinning top and the constant force is gravity. We have a spinning top where due to friction it slowly losses momentum, at some point it will tilt and the force of gravity acting through the spinning tops centre of gravity will create an implied new axis? and as gravity is not at any fixed point, but continues to act no matter where the top is, the result is the top will slowly gyrate with the axis moving around in an ever increasing larger circle, so the observation I would like to make here is, is the loss of angular momentum in the top at this point due to friction or gravity?

Regards JD.

with multiple axes and rotation changes you get all manner of complexity, precession being the main byproduct and a football has all it's mas concentrated at the edge with close to zero in the middle, = worst case for this situation.

A complex tumbling motion will ensue. In the shuttle they analyze into vectors and try to cancel each axis bit by bit, but it is no simple task to figure out, and it is hard to do by seat of pants as too many things happening at once

sub atomic particles do not really spin... At least according to quantum physicists.

Every thing in the universe seems to rotate about some axis, but when it comes to sub atomic particles the same rules don't apply. I find that very strange, they move in orbits and forces seek out positions of equilibrium. But if thats what they say, with my knowledge of the subject, they must be right? Thanks for the insight.

Regards JD.

I agree... It sucks giving the devil his due, but at least up to this point, quantum physics has produced more understanding (and technologies) out of physics than just about any other approach. And while there are many scientists standing in line to write articles to bring enlightenment to the layman regarding classical physics and even Relativistic physics, it seems as though the quantum physicists have taken the position, "Why bother. They wouldn't believe us even if we told them!" As a result, the mountain must go to Mohammad!

So for some more quantum weirdness, subatomic particles do not orbit each other, either. We call quantum states of electrons "orbitals" as a convenience, but, in reality, this is not the case. electrons are bound about atomic nuclei in energy levels or states, but if you go there with a quantum physicist... Well, it's kinda like "Alice Through the Looking Glass" in that realm.

The fly and ball is a conservation system at first. the angular momentum is a constant. so we get
mw + Jw =C
where m fly mass and J ball moment of inertia, w fly anular speed and w ball angular speed. v = rw, r ball radius, as the v is always tangent vector, the ball is applied by a tangent force,evenif its very tiny. so the ball will be rotation around its centre.
regard to earth coordinate, the system will has a movemetn, say free drop. and vector is V
so the fly has vector of v + V.(theyare all vector)

or vx1+Vx=vx1
vy1+Vy=vy1
vz1+Vz=vz1+Vz

suppose coordinate1 parallel earth cooordinate. if not, add rotation transform.

From this we can get the result of when a man walk in a space ship.

this can relate to a man walk on the earth.

to find a mans trace in space. ( in sun system and milk way system etc.)