Waterwheel at Llanberis Slate Museum

It took 45 seconds for the wheel to complete one full turn. The diameter is 15.4 metres. That means the rim has a linear velocity of 2*pi*r/T = 1.1 metres per second. It all seemed to be moving so slowly but that is the speed of the a fast sprinter.

Is this a voltmeter?

This meter has no units so what is it measuring? I'm assuming that it is a voltmeter measuring the emf generated by placing your hands on the different metals. https://www.exploratorium.edu/snacks/hand-battery This site explains that the electrolyte is actually the sweat on your skin which allows the metals to give and receive electrons. The aluminium is more reactive so it finds it easier to lose electrons to form positive ions. Copper finds it harder to lose electrons so there is a net flow of electrons from aluminium to copper. https://www.mpoweruk.com/chemistries.htm

Why they are called sails on a windmill

The board above explains that windmills were turned by a wooden framework over which a sail was spread. In very windy conditions, you could wrap up the sail so the wind was catching less of an area and so providing a smaller force. I like the solution with spring-loaded shutters. A stronger wind puts a bigger force on the spring, opening the shutter and letting some of the wind straight through.

Notice that the windmill has been done with two of each. And notice that they are diagonally opposite each other. The spring loaded sails will adjust to wind strength automatically whilst a human has to make a decision on the canvas sails. This could lead to uneven torques if different types are paired up. I suppose that the diagonal pairings act as a couple in the technical sense.

Lightning conductors in windmills

The end of the sail on Green's Mill appeared to have a lightning conductor on it. I'm wondering how that connects to the earth given that the contact must be rotating as the sails turn. It could be done with carbon brushes like in an electric motor. I read of one old wind powered corn mill that survived a lightning strike when the current was conducted down an external chain used to raise sacks of corn. Lightning strikes on modern wind turbines are a big topic https://www.windpowerengineering.com/preparing-turbines-for-lighting-strikes/ has some good information. I was interested to read that the average energy release is 55kWh, in other words, enough to run my convection heater non-stop for two days. It also says that static charge is generated in the metal blades as they sweep through the air. There must also be some kind of emf between the blade tips and the centre, but that needs a separate post.

Chaotic pendulum at Green's Mill

 This chaotic pendulum was at Green's Mill in Sneinton. It consists of a magnet on a rod above 3 other magnets, which it cannot quite reach. Notice that the socket for the rod is not above the centre of the magnet disc, which can be rotated.

 Further inspection showed that the swinging magnet attracted to one of the magnets below but was repelled by the other two.

The magnet describes an oscillatory motion but it should never fully repeat itself even if released from what seems to be an identical position. This is what it means for a system to be chaotic. A normal orbital motion goes round and round endlessly and predictably repeating itself. The weather goes in cycles, doing roughly the same thing at the same time every year but never fully repeats itself. This magnet will always settle over the attracting magnet at the end as it loses energy. The weather often settles into certain patterns that seem hard to shift. These patterns would be called the attractors of the the system. At the moment, we seem stuck in a pattern of very rainy weather over the southern UK. However, just as I could put some energy in to knock the magnet out of its attractor state, something will eventually inject the energy to knock the weather out of this attractor and it will settle into another state.

Green's Functions

Green's Mill was run by the mathematician George Green. I finally understood Green's Theorem after 30 years http://wigtonphysics.blogspot.com/2018/01/greens-theorem.html and so was keen to go back to the mill. I wanted to see the Local Heroes film by Adam Hart-Davies which uses clockwork toys to explain aspects of the theorem. I looked for it on the Internet when I was trying to understand the theorem but couldn't find it. They still have it playing. But they also have this film about Green's Functions https://www.youtube.com/watch?v=ji-i6XCkgC0. No wonder I cam across them when I was working on perturbation theory in quantum mechanics. If you disturb a linear system in one place, they allow you to calculate the effect time T later in another place.

GCSE required practical to prove the wave equation

I'm interested that it been suggested that the stationary wave demonstration should be used to illustrate the equation wave speed = frequency x wavelength as well as the ripple tank. It requires explaining that two "loops" make up one wavelength and requires trust that the wave speed remains constant if the same tension is on the string. It can then show that if you double the frequency, the wavelength halves (ie number of "loops" doubles). It's the first time I've tried it with weighted string. I've previously used a clamped piece of thin rubber tubing. On the string, I could only get 4 "loops" but I've have up to 8 on the rubber tubing.

Centrifugal governor at Green's Mill

We visited Green's Mill in Sneinton. The governor was invented by Christiaan Huygens for this purpose of ensuring the flour was evenly ground. The adjuster arm for the millstone separation has manual control on one end with the T-bar screw and the governor is the automatic control at the other end. As the mill spins faster, the heavy balls are dragged round faster. Their inertia causes increased tension in their angled supports. Since their weight mg=Tsin(theta), where theta is the angle to the horizintal, if T goes up, theta must go down. In other words, the balls tend to be nearer to the horizontal when they go faster. If you look, this would act to pull upwards on that adjuster bar.

Pigeons in space-time at Stonebridge City Farm

The way these pigeons were making the netting sag at the farm in Nottingham reminded me of the way that masses cause space-time to curve in Einstein's General Theory of Relativity. Fortunately none of them was heavy enough to cause a black hole.

After the chocolate

I really enjoyed the hot chocolate made by this machine and was keen to investigate. It turns out that the stirrer is held in magnetically. There must be a rotating magnet or some kind of induction motor effect in underneath. Previously there would have been a sealed spindle up from the motor below but that would still have left joints down which liquid could seep. I first saw magnetic stirrers in the lab nearly 30 years ago so it is interesting to see that they have now made it into the kitchen.

Henley's electrometer

I found this electrometer in the Whipple Museum in Cambridge. In terms of analysis I normally use two balls with identical charge on threads - a symmetrical problem.

So how do we model the Henley electroscope? Will the ball and the the central pole have the same charge? It looks like a rod not a string. Does that make a difference? Anyway, here's my first sketch:

I don't know whether the electroscope was to show relative charge or actual charge using Coulomb's Law but the latter looks possible once the angle is known.

Curved space-time and Hawking

I suppose that the fame that Einstein attracted a century ago has been mirrored in our own time by Hawking. The are linked by curved space-time. Einstein's equations described it. Hawking studied the black holes that came out of the equations. These days we describe space-time as like a sheet of Lycra with a bowling ball on to represent the mass of a star. Sadly I've never had a large enough sheet of Lycra to do it. 50 years ago Hawking had these models made. The top one shows the way a star (the yellow centre) dents space-time. The bottom one shows that a black hole does something very extreme to the space-time.

Whatever next?

Well, it turns out this variety was named in the 1940s when Einstein would still have been alive. It shows his reach in popular culture!

Useless protractors

I liked this display in the Whipple Museum of the History of Science  in Cambridge. You can't use these lovely coloured protractors because you can't see the measuring point through the opaque plastic!

Decimal clock

 This is in the Fotzwilliam Museum in Cambridge. If there were 10 hours in a day, each decimal hour would last for 144 of our normal minutes. Nearly two and half normal hours! Each decimal minute would last for 86.4 normal seconds. The decimal hours would seem ridiculously long compared to normal hours but decimal minutes and decimal seconds might not seem so far out.

Not Newton's Apple Tree at Trinity College, Cambridge

I was excited when I saw that Newton's apple tree was outside Trinity College, Cambridge but a little perplexed as well because I have visited it at Woolsthorpe Manor. This is actually a graft from the original tree http://www.creatingmycambridge.com/songs-creative/resources/local-history-topics/newtons-apple-tree/

Four years later and the pattern is still there

There was a pattern in this gill on the slopes of Rest Dodd when I last went past four years ago http://wigtonphysics.blogspot.com/2015/08/interesting-wave-like-pattern-in-gill.html It was in a slightly different part of the pool but was still there. This time I could see progressive waves moving through the pattern. There is a vertical stone at the back which would reflect them so this should be a good site for a stationary wave to appear so perhaps the pattern shows nodes and antinodes. It has occurred to me that I could test this hypothesis in the lab by setting up a ripple tank with a reflective barrier and adding detergent.

Cyclotron

The few times that I have seen a cyclotron I have been surprised about how small it is. It is in the order of 30cm diameter. It is one of the earliest particle accelerators. The two metal halves are called Ds. The Ds are metal so that they can be given an electric potential. Hence there is a potential difference across the gap. positive particles are injected into the centre. A strong magnetic field acts perpendicular to the D - ie into the plane of this picture. The magnetic field is perpendicular to the motion of the charged particle so by Fleming's Left Hand Rule a force acts of the particles which acts towards the centre and pulls the particle round in a circle. The potential difference is alternating so that when the particle completes a half circle and returns to the middle, the potential switches which accelerates the particle across the middle and into the other D. Each time the particle crosses the middle, it gets faster and so orbits at a bigger radius. The clever thing is that no matter what the radius, it takes the same time to complete a half circuit so all particles in the apparatus can be accelerated at the same time. The limit on the size is that if it were biggest, relativistic effects would increase the mass and thus cause a particle to go more slowly, not reaching the middle at the same time.