Interesting fact about a wheel.

**Patar** · 18th February 2008, 16:47

Originally Posted by GSVR

So you agree with what I'm saying here? That the top half of the wheel carrys almost 4.5 times the momentum of the bottom half at any speed.

You're point of view is from a stationary position on the ground which is wrong, at least if you are considering the effect it has on the bike. Imagine the bike to be floating in mid air and the wheels are spinning at an rpm equal to 100kph, it is easy to see that both the top and bottom of the wheel carry equal momentum as relates to the bike.

If you get hit by the wheel of a bike then yes the top of the wheel would be carrying more momentum than the bottom, but i fail to see how that would be relevant as there would be bigger things to worry about.

**Mikkel** · 18th February 2008, 16:50

Originally Posted by GSVR

When I was at intermediate school many years ago a teacher was explaining electricity to the class. His theory was that cables had many strands to carry more power as electricity only moved over the surface of the wire.

I'll make no excuse for teachers who don't understand the rudiments of their subjects!

I'm actually not concerned about any gyroscopic coupling here its something that doesn't come into this equation. All its about is measuring momentum in one direction.

If you want to know the momentum the rotation is irrelevant. You want the momentum of the wheel in the setup on the train?
Easy - it's just the product of the mass and the velocity of the centre of mass (in this case it's 100 km/h when seen from an inertial FoR).
So if the wheel weighs 10 kgs - the momentum is 277.8 kg*m/s or 277.8 N*s.

**Badjelly** · 18th February 2008, 17:04

Originally Posted by GSVR

I'm actually not concerned about any gyroscopic coupling here its something that doesn't come into this equation.

Maybe not, but gyroscopic effects do come into play when you start changing the direction of the wheel's axis of rotation, or when you talk about the stability of the wheel to such changes.

I think that if you followed down the route of considering the difference in linear momentum between the top and bottom of the wheel, and its effect on the wheel's dynamics, you could eventually reinvent the concept of angular momentum. Better to accept that this concept was invented 200-odd years ago and has been developed and tested since then.

**GSVR** · 18th February 2008, 18:39

I do actually agree with pretty much all that you guys have said.

There must some flaw in what I've said and calculated. Saying you can't look at two halves in isolation doesn't actually work for me becuase I already have.

Yes its so easy just to get the wheels mass and multiply it by the velocity. Breaking it down further may be pointless but it does demonstrate that although something appears to make perfect sense on paper in reality it could be totally wrong.

Liked the Einstein example Badjelly but when your in a train don't you find it slightly easier to sway from side to side if your looking out the window as opposed to down the corridor? To accelerate from side to side might be a better term to use

**GSVR** · 19th February 2008, 08:19

Ok heres a final train carriage example.

All the figures are the same as the last one just the pivot point has changed. The pivot passes through where the contact patch would be on the road if the wheel was on the motorcycle. I'd better also say the the red pivot points are bolted solid to the carriage deck.

Two experiments:

One with the wheel revolving the direction indicated in the drawing.
The other with the wheel revolving anticlockwise.

Does one require more work. (moving the mass though the same angular movement in the same amount of time) than the other.

**Badjelly** · 19th February 2008, 09:04

Originally Posted by GSVR

Two experiments:

One with the wheel revolving the direction indicated in the drawing.
The other with the wheel revolving anticlockwise.

Does one require more work. (moving the mass though the same angular movement in the same amount of time) than the other.

Actually, neither requires any work at all, using "work" in its technical sense. There are 2 equivalent ways of looking at work. One is that work done on a system changes its energy. If I take a spinning wheel and change the direction of the axle, the wheel does not spin faster or slower, so no work has been done. The other way of looking at work is that it is equal to the force applied multiplied by the distance moved in the direction of the force. If you take a spinning wheel, grab the axle and change the orientation of the axle, there will be forces generated due to the rotation of the wheel, but they will always be at right angles to the movemement. So again, no work. (We had to get the same answer using both ways of defining work, because they are equivalent.)

Try this:

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

Furthermore, whatever question you are asking about the behaviour of your hypothetical wheel in your hypothetical train carriage moving at constant velocity, the answer doesn't depend on the speed or direction of movement of the carriage. Really.

**GSVR** · 19th February 2008, 09:30

Maybe I choose the wrong word there. Effort?

Lets just say that the angular side to side travel is limited to 30 degrees against solid stops. The assemby is resting on one stop and a constant force applied till it hits the other stop. The time taken for this to happen is accurately measured.

Then the direction of the wheel is reversed and the same experiment done.

Will these times be exactly the same or will they be different?

**Badjelly** · 19th February 2008, 09:34

Originally Posted by GSVR

Maybe I choose the wrong word there. Effort?

Lets just say that the angular side to side travel is limited to 30 degrees against solid stops. The assemby is resting on one stop and a constant force applied till it hits the other stop. The time taken for this to happen is accurately measured.

Then the direction of the wheel is reversed and the same experiment done.

Will these times be exactly the same or will they be different?

If I understand you correctly, exactly the same, as the only thing you change between the 2 experiments is the direction of rotation and there's nothing in the experiment that would be affected by that.

You might like to read this again:

Furthermore, whatever question you are asking about the behaviour of your hypothetical wheel in your hypothetical train carriage moving at constant velocity, the answer doesn't depend on the speed or direction of movement of the carriage. Really.

Really.

**Badjelly** · 19th February 2008, 09:42

Originally Posted by Badjelly

Furthermore, whatever question you are asking about the behaviour of your hypothetical wheel in your hypothetical train carriage moving at constant velocity, the answer doesn't depend on the speed or direction of movement of the carriage. Really.

To back this up, the Earth is moving through space at some tremendous speed. What effect does this have on your wheel in your train carriage, or on the handling of your motorcycle? The Earth is also rotating (1 rpd) and this does have effects on winds and ocean currents, that I spend most of my working life calculating. But the linear movement has no effect whatsoever.

**GSVR** · 19th February 2008, 10:04

Thats great so now we can comfortably say that anyone who reads this thread should get it as its been totally flogged to death by me.

Lets move on to something else now the two threads have been merged.

Going from the calculator in the very first post:

55rpm is the revolutions required for 1g about a 0.6m wheel (0.30m radius)

55 rpm times 1.884 metres (circumference) equals 103.62 metres per minute or 6217.2 metres per hour (6.2 kph)

So at around 6.2 kph the part of the tyre at the top of the tyre is in equalibrium with the 1g of gravity and is infact weightless.
And also the part of the tyre at the bottom is experiencing 2 g of force (gravity plus the centrifugal force)

Comparing this to the 200 and something g at 100kph its seems insignificant.

**scumdog** · 19th February 2008, 10:15

Originally Posted by Mikkel

I'd say you'd have to go fucking fast for that to happen - but indeed, why take a chance? Send Mythbusters an email - would be interesting to see. I guess they might take a motorcycle wheel and indeed rotate it at 14,000 RPM with the cap off to see if it deflates...

It's true, a Kiwi drag racing team back in the day had problems with the front tyres on their rail deflating with each run, they found out the valve spring pressure was being overcome by the centrifugal forces.

Simply putting on valve caps fixed the problem.'

**GSVR** · 19th February 2008, 10:56

I think most people have rolled a hoop or a tyre down the road and at a certain speed it will stay upright by itself.

For a hoop of 0.6m diameter would this be when the hoops speed exceeds 6.2kph or would the actual speed be somewhat lower! I'm pretty sure anything above 6.2 kph maxium effect has taken place and the forces holding it upright will be will the same. But I'm also sure others will say the faster it goes the greater the gyroscopic forces are and these also hold the wheel upright!

Read my last post if you need more info.