Monday, 23 January 2012

My Gyroscope won't fall down - I

I love this video
and used to do this very demo when teaching classical mechanics. But here's a question for you - why doesn't the wheel fall over?

If you trawl the text books, even the wonderful Feynman Lectures on Physics (a must read for any serious student of physics), the answer given is that the wheel doesn't fall down because of the conservation of angular momentum.

Alas, I think this answer is a bit of a cop out, and doesn't answer the question. Why? Let's consider the collision between two cars. We know from Newtonian mechanics that momentum is conserved, so the momentum before the collision is exactly the same as after the collision (let's ignore external forces for now, imagine the collision is on a frictionless sheet of ice).

The conservation of momentum is a consequence of Newton's third law, and in the collision all of the forces acting have equal and opposite reaction forces, with the total momentum unchanged. Basically, considering the conservation of momentum lets you ignore all of the forces going on in the collision.

But if you are one of the car drivers, you care implicitly about the forces acting, as you would very much prefer a gentle force acting on you over a long period (as provided by an air bag) as opposed to a larger force over a short period (as provided when your head hits the dashboard). 

The situation with the wheel is similar, as the action of the internal forces (well, torques) act so that the total angular moment is conserved. But really, to understand what's going on here, the question you should be asking is "what force is holding the wheel up?".

I know the answer, but would like to demonstrate it with a simplified model. Alas, the simplified model is not that simple, and it's going to take a few posts to get through, but basically I'm going to make a computer model of a wheel, spin it, let it go and look at where the forces are.

But firstly, a truth about the universe, namely that it is made from particles and springs
(taken from the excellent webpage of Paul Bourke, a place with excellent graphics advice). Now, this might sound weird, but you can represent physical material, and how they move etc, as a system of masses connected by springs. Check this out
and read the tutorial here. I wish I had realised this when I did my course on vibrations and waves as an undergraduate :)

So, my simplified version of a wheel will be four masses connected to an axle, and to each other, by springs. The forces in the springs will effectively represent tensions in the wheel. I'll add a force due to gravity (pointing downwards) and the force on each spring will be represented by Hooke's law. This simplified model already has 24 variables! Three position and three velocities (in 3-d) for each mass.

You can derive the equations of motion either using standard Newtonian forces, or a little more neatly using a Lagrangian approach, but I won't write the equations here, but will save them for another post.

So here's my basic wheel. All I've done here is stretch the springs and let the thing oscillate a little Don't forget that gravity is acting downwards, which is why it is asymmetric.
OK, we can remove the stretch. But how is this a wheel. Well, let's give one of the masses a tangential push. Let's take the black mass and push it upwards.
The net effect is that the entire distribution of masses starts to move, and the wheel is rotating. Of course, it looks a little springy and bouncy, but it's how a real wheel works; all the internal masses of the wheel are talking to one another through internal forces. If we tighten up the springs a little, we can get it to be less bouncy.
Excellent. Well, at the start! But then things go pear-shaped! What's happening? Integration errors, that's what! Basically, I am using a Michael-Mouse integration scheme for these initial tests (and Euler scheme for those in the know) and small errors build up rapidly. What we end up with is energy not being conserved and madness ensuing.

But we can fix this up with a better integration scheme. I'm going to leave that to next time :)

Friday, 13 January 2012

Anglo-Australian Bowie

For a long time, I have been a fan of David Bowie, and have seen him in concert a couple of times. In the good old days (early 1980s), when MTV showed nothing but music videos, I would happily while away the hours on Bowie (and Queen, and just about everything else).

But as everyone knows, people grow-up and have to go to university, and MTV went the way of pathetic shows rather than showing videos, and so I didn't really watch music videos any more.

While holidaying last week, we happened to be chilling, and decided to watch a bit of Rage as they were showing a series of Bowie videos, and while watching Let's Dance, I had a "ehh - that's familiar" kind of moment. It was driven by this image
a sight what will be familiar to astronomers the world over. No, not the people in the foreground, or the nuclear explosion in the background, but the mountains!

Why? Because they are the mighty Warrumbungles, mountains in Northern(ish) New South Wales, near the town of Coonabarabran. Why would these mountains be familiar to astronomers? Well, Siding Spring Observatory, home of the Anglo-Australian Telescope (the largest optical telescope in Australia, a world-beater in surveys of the heavens, and where I used to work), overlooks the park.

The thing that caught my eye is not just that these are the Warrumbungles, but the mountains look virtually the same as seen from the catwalk of the telescope, or the look-out point at the edge of the observatory.

Here's a view from the base of the AAT
(the red thing is the case that the 3.9m mirror was carried to the observatory in), and here's another view
So, I got a little excited! What if David Bowie had visited Siding Springs (and the AAT); I know it's not really a lot to get excited about, but at least it was something to think about.

My hopes were a little dashed after a little detective work. The clip in the video was not filmed on Siding Spring mountain, but actually White Gum Lookout in the National Park.
But why are the views so similar. This map explains it all
The look out basically sits on the line joining Siding Spring Observatory and the lovely peaks of the Warrumbungles. Apparently Bowie visiting Coonabarabran in the early 1980s was big news at the time (but the person who told me this kept well away). Ah well, even if he didn't visit the AAT, David Bowie must have driven close by :)

Wednesday, 11 January 2012

Weightlessness

Sorry for the delay, but I've been off on a family holiday, touring and camping in New South Wales (which doesn't look a lot like the old version), coupled with a trip over the border into alien territory, namely Queensland.

I was on the Gold Coast, a tourist mecca and home to a number of theme parks. As the father of little-cusps, we headed to DreamWorld to be thrown about a little. When I was riding the Cyclone....
I remember a post a long time ago by my ex-Honours and MSc student, Luke Barnes (who has just returned to an Australia as a Super Science Fellow), namely what does it feel like to be weightless.

Of course, what I mean by weightless is something like this,
namely some astronauts cavorting about in orbit, floating about and just having a good old time of it.

So, what does weightlessness *feel* like? Many have seen astronauts training, in their gear, in water tanks. They can bob about and look something like this
Doesn't that look nice and peaceful? I know they have a job to do, but bobbing about in water is relaxing. Look, lots of people do it!
Gee, astronauts have it easy.

But is that is what weightlessness really feels like? Well, no.

When you are bobbing about in a pool, even in an astronaut spacesuit, you *feel* gravity, and you know what direction it points in. Gravity pulls you towards the centre of the Earth. When you are floating "head-up", your guts are pulled down towards your legs, as is your blood and other fluids. There are force gradients across your muscles, and basically you feel the direction of gravity.

If you closed your eyes and someone gently rotate you onto your side, you would sense it. Your guts would slosh over and put different pressures on your body, as would your blood flow and the other processes in your body. You would know that your body's orientation with regards to the gravitational field has changed.

However, a spaceship orbiting the Earth is in free fall, continuously accelerating towards the centre of the planet, but getting no closer.
What is this free fall like? Well, those who have been on a roller coaster, or up-and-down road, know what free fall feels like. But let's look at what Einstein told us. Basically, he encapsulated this in the equivalence principle. Essentially, what this says is that for someone free falling in a gravitational field, the effects of gravity disappear (we'll ignore the subtleties of tidal forces).

What this means is that, without a gravitational field, your body has no clues on what way is up. Your guts hang there, not pressing down or up, or side ways, but just hang there. Your gravitationally induced stresses in your muscles vanish, your blood pressure gradients change. Basically, your body has no clue to up.

What it feels like is going over the top of the roller coaster with that unpleasant feeling of your stomach in you mouth. Or more like this ride
but instead of the feeling of falling for seconds, the sensation goes on for minutes, hours, weeks and months.

No wonder some astronauts throw-up when they get into space!! Floating it is not!