Leap-second day

Remember to put your clock forward by 1 second at midnight tonight. It's leap-second day. Time measurement in Physics was traditionally based on the movement of astronomical bodies - that's a very human thing. Unfortunately, the cycles don't quite match up. A day is one rotation of the Earth about its axis. A year is the journey round the Sun. There isn't an integer number of days in a year; hence the leap-year. But the rate of rotation of the Earth has been slowing down for billions of years. This is due to the effects of tides. There never was a problem because clocks were set by 12 noon being the time at which the Sun was highest in the sky. But the need for ultra-precise timing meant that atomic clocks were introduced. These define a second as a particular large number of oscillations of light from a particular energy level jump in caesium-133. An energy level jump means that there is only one very precise frequency involved. Most timing devices now run from atomic clocks. But human "Sun-time" falls out of step because the rotation of the Earth is gradually slowing. They first put in a leap-second in 1972 and I think they said this was the 27th leap-second added. In other words, atomic clocks would have had midday out by nearly half a minute now if uncorrected.

A moment of inertia in Ravenglass

I had a chance to test out the conservation of angular momentum! Linear momentum = mass x velocity. Angular momentum = moment of inertia x angular velocity. Moment of inertia is a combination of the mass and how far away it is from the centre of rotation. The further a mass is from the centre, the harder it is to turn. So I got the roundabout spinning and lent outwards. The rotation slowed down because a larger moment of inertia means smaller angular velocity. I then lent in towards the middle and the rotation got faster because the moment of inertia had decreased. Angular momentum was conserved because moment of inertia x angular velocity remained the same throughout. It's like spinning skaters speeding up when they pull their arms inwards.

Preparing for L6 Physics #2: Weight and moments on Green Crag

We found this boulder high on Green Crag. There's a nice view of upper Eskdale! I was asked how long a lever would have to be to lift the rock. This raises 4 L6 Physics issues:
1. Estimating sizes. I'm sorry that I forgot to put any scaling objects in the picture, but the rock was maybe 1 metre high, so let's say the volume was 1 cubic metre. You need to be able to do things like this.
2. Density is the mass per unit volume. 1 cubic metre IS unit volume. Looking up rock density on the Internet, it's about 3000 kg per cubic metre. (1000 kg is 1 tonne) http://geology.about.com/cs/rock_types/a/aarockspecgrav.htm So this rock is as heavy as a car.
3. Are you confident with the difference between mass and weight? Mass is a measure of the stuff things are made of; weight is the pull of gravity on the object. Mass is in kg; weight is in Newtons. Weight = mass x g, where g is gravitational field strength, taken as 9.81 N/kg in Physics. So the weight of the rock is 29430N.
4. The Principle of Moments: a moment is a turning force. Moment = force x perpendicular distance from the pivot. Say we put a pivot 1 metre from the rock and I stood on the other end. I would just be lifting the rock when the moments were equal. Moment for rock = 29400N x 1 metre. Moment for me = 650N x d metres. So how big is d? d = 29430 x 1 /650 = 45 metres. That's a big lever!

Preparing for Lower Sixth Physics #1

If you're going to start Lower Sixth Physics in September, it would be good if you watched some of the lectures by the legendary physicist Richard Feynman. He was a Nobel Prize winner and he was also a wonderful science communicator. http://research.microsoft.com/apps/tools/tuva/index.html

Try Minute Physics on Youtube: Physics in 1 minute!     https://www.youtube.com/user/minutephysics

MIT is one of the best universities in the world. Here is their Physics video channel   http://video.mit.edu/channel/physics/ 

I really recommend the Smarter Every Day channel on Youtube. Try this film for a start. It's awesome! http://www.smartereveryday.com/toiletswirl/

I'm trying to understand university Physics using this site. If you're interested in weird stuff like General Relativity, Leonard Susskind is a smart guy http://www.openculture.com/2013/05/leonard_susskind_teaches_you_the_theoretical_minimum.html

I will be posting stuff about Lower Sixth topics on this blog during the summer. If you want to get ahead, check out last summer's stuff from last July and August.

See you in September!

I

Fickle Steps - stationary waves on the Duddon

This is Fickle Steps up the Duddon Valley past Seathwaite. We liked the steel hawser to guide you across. I found that it was possible to oscillate it at different frequencies to create stationary wave patterns. Firstly, slow vibrations gave the basic skipping rope pattern - that's the fundamental frequency. Gently vibrating it at twice the frequency - it proved easier to judge than I thought - produced the first overtone which has a fixed point called a node in the middle. That's shown in the bottom picture. I did get the third overtone but judging the frequencies is hard. It works because the initial vibration reflects from the fixing at the far side. The incident and reflected oscillations interfere to produce the fixed pattern.

Trebuchet at Urquhart Castle

Here is the reconstructed trebuchet at Urquhart Castle on Loch Ness.

 Seen in the photograph below, it is easier to understand.

 The arm is settled so that the long bit is close to the ground, and it has a heavy ball like the one below in a sling attached to the arm. Then a much heavier load is put in the wooden cradle on the right. Since there is no balance, the wooden cradle will fall, rotating the arm. Both sides of the arm rotate with the same angular velocity, but it is the linear velocity of the heavy ball that will be most important. Linear velocity = angular velocity x radial distance from the pivot. Since the ball is about five times further than the cradle, it will have a high linear velocity when it is fired. It is a bit more complex than this because the ball is attached by a string and sling, so there are whiplash effects.
                                          

Wearing away: Falls of Foyers

These are the lower Falls of Foyers by Loch Ness. I was struck on my previous visit by the V-shaped notch at the top of the falls. The total height of the waterfall is given as 62 metres. It's hard to photograph the whole thing. I think that the notch must be about 20 metres deep. I have reasoned that water cannot have flowed down here until after the last Ice Age given that glaciers must have been carving the edges of the Great Glen at that point. So water can only have been flowing this way for about 10000 years. 20000mm divided by 10000 years would mean a rate of attrition of 2mm per year. That's not unreasonable.
The falls really impressed a visiting Robert Burns who wrote a poem on the spot:

Stationary wave: Fourier series in Radley churchyard

The hedge in Radley churchyard is a wave that isn't going anywhere. If you didn't know, Radley is a village near Oxford, The wave is a type called a saw-tooth wave. The mathematician Fourier showed that all complicated wave shapes like this could be made by adding together rounded sine waves of different frequencies. This wave has a particularly vicious equation  http://mathworld.wolfram.com/FourierSeriesSawtoothWave.html but this page does have a picture showing how the rounded waves make up the saw-tooth.

Sun dial makes history in St Peter Port

I've blogged about a few interesting sundials. This one is more like a "history dial". It only tells the time on one day a year - May 9th - the day Guernsey was liberated at the end of the war. The shadow moves along the bench and tells you what was happening at that time of day on 9 May 1945. Since it only works on one day a year, there is no need for a gnomon of a particular angle. The only problem is that it needs to be sunny on 9 May every year. We were there on the wrong day but at least it was sunny. The Sun is higher in the sky in June so the shadow fell short of the bench.

Solar water heater at Samye Ling

There was a display about the solar water heaters at the Buddhist centre near Eskdalemuir.If you follow the pipework on the left hand side of the diagram there is a countercurrent heat exchanger. Cold water flows into the bottom of the panel. This is because the solar heat radiation raises the temperature of the water making it expand and become less dense. Hence it tends to rise by convection. Best to have the water moving in the direction of the natural current. But notice that the hot water pipe then goes into the middle of the hot water tank and goes downwards. This seems odd because a kettle heats water from the bottom. Given that colder water in the tank will tend to sink, it is best to heat water in the middle first. That lowers the temperature of the solar heated water. If it comes into contact with colder tank water at the bottom of the tank, there will still be a temperature gradient to deliver more energy to the tank. The flow of the solar-heated water is opposite to the direction of any warm convection currents in the water.

Definitely alto

I was musing last month about altocumulus cloud on the Lincolnshire coast. I photographed this at Loch Ness. You can clearly see that there are two cloud layers and that the rippled layer is the higher of the two. The wind was moving in different directions in the different levels and at times it was hard to tell which layer was moving. The lower cumulus layer was just above the highest local mountain and so might have been 800 to 1000m. Altocumulus is between about 2000 and 6000m.

Angular velocity: prayer wheels at Samye Ling

We visited the Samye Ling Buddhist monastery at Eskdalemuir in southern Scotland. They have a building full of electrically turned prayer wheels. I forgot to time the rotation but it was about 20 seconds. Angular velocity is not the metres covered per second, but the number of degrees. And actually, we don't use degrees, we use another measure of angle called RADIANS. There are 2pi radians for every 360 degrees - that's about 6.28 radians. So a complete circle in 20 seconds would mean an angular velocity of 6.28/20 = 0.314 radians per second.

Crossing continents: a trip to Langholm

These are views from the Malcolm monument on Whita Hill above Langholm in southern Scotland. You can see our house in the views - well, I could pick out Wigton's factory through the binoculars. You can make out Skiddaw in the bottom photograph. And you can see Whita Hill and its monument from my garden. I was amazed to discover some years ago that Wigton and Langholm were on separate continents until 450 million years ago. Between us was an ocean called the Iapetus Ocean. It's roughly where the Atlantic Ocean later opened, so it was named after Iapetus who was the father of Atlas (Atlantic...) in Greek mythology. The hills on either side of the Solway weren't there when there were two continents. In fact, the hills were still mud on the edge of each continental shelf. They formed mudstones which were pushed up and metamorphosed into slates and the amazingly named greywackes due to the pressure of the collision. So Skiddaw used to be mud on the bottom of the ocean. As did these hills in the Southern Uplands taken from Bailiehill hill fort near Eskdalemuir. You can see the crumpling of the landscape caused by the collision.

It's the nearest I'm likely to get to crossing continents!

Boundary conditions

 

                                       
Here's the new fence I've been building. Boundary conditions play an important part in Physics. The laws of Physics are very general. In fact, they were often stated as proportionalities. For example, Newton just said that acceleration was proportional to resultant force. To make the differential equations fit one particular example, particular numbers need to be inserted. These are often called boundary conditions. eg speed at time zero. http://hyperphysics.phy-astr.gsu.edu/hbase/diff.html#c4  Another boundary problem I've come across this year involves the setting of coordinates in abstract mathematical spaces. These can often have many dimensions. x and y axes don't work well when the space is curved, so the space is often thought of as being sections of flat x,y planes that are patched together; hence the boundaries. I've been trying to understand tensors, which I think are going to be independent of the choice of local coordinates and allow you to make transformations within the mathematical space.

Odd lightning conductor at Urquhart Castle

The big tower at Urquhart Castle on Loch Ness had an interesting lightning conductor. A little Internet research suggests that some of the things I thought I knew about lightning conductors might be myths, so more research needed. I know that a sharp point concentrates the charge and makes for a bigger electric field strength at the tip. With a Van de Graaff generator, you also get a noticeable electric wind being pushed away from the tip. The concentrating of the electric field means that you are more likely to reach breakdown field strength there, making a strike more likely. I have read that there is some controversy over whether ball shapes might be better. This design seems to be hedging its bets. Maybe 3 spikes gives 3 chances for a reaching of the breakdown field strength. I saw one uncorroborated suggestion that it stops a strike leaping from the spike to the roof.

Coriolis Effect at Loch Ness Shores

The Coriolis Effect is what makes hurricanes spin anti-clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. Sinks are supposed to drain in the same way but I know that there are too many variables to do with basin design and initial conditions. So I was really pleased to see that the washing up sinks on the Loch Ness Shores campsite behaved! I was just getting ready to post about this when I was tipped off about another brilliant piece from Smarter Every Day. You really must watch this. I wish I'd had the Coriolis Effect explained at university as clearly as it is explained here http://www.smartereveryday.com/toiletswirl

Precision in the New Forest

We stopped at Burley in the New Forest on our travels. Precision on a measured scale is supposed to be +/- half a scale division on a scale. That would mean a precision of +/- half a minute for the minute hand. But that depends on the mechanism. I didn't watch this clock for long enough but some similar clocks have a mechanism that jolts the minute hand forward at the end of every minute. It isn't a smooth motion. A clock that jolts the hand forward like that has more in common with a digital measuring instrument. In that case we'd only be able to say +/- 1 minute.

Thinking about dolphin buoyancy on Chanonry Point

We were back on Chanonry Point near Inverness to watch the dolphins. Marvellous! I got to thinking about floating and sinking. When you get into water, you push water out of the way: we say that the water is displaced. You can catch the displaced water and weigh it. When you get into water, you feel lighter. This is because there is an upwards force on you called "upthrust". That's your buoyancy. Archimedes showed that the upthrust is equal to the weight of the displaced water. By weight, I mean the pull of gravity on that mass of water, measured in Newtons. If the weight of displaced water is more than your own weight, you float. You and the displaced water will occupy the same volume but the displaced water will have more mass and thus you will be less dense than the water. A dolphin can make this happen by filling its lungs with air. I found an excellent article on the various factors that can affect buoyancy in dolphins: http://www.dolphincommunicationproject.org/index.php/2014-10-21-00-13-26/dolphin-science-factoids/item/94360-do-dolphins-float-or-sink

Bake off: entropy increases

I baked a cake for Mrs B. I've posted before about entropy. Entropy is said to be a measure of the disorder of a system. The more disordered, the higher the entropy. The Second Law of Thermodynamics says that entropy will always increase. I've posted about this before - see http://wigtonphysics.blogspot.co.uk/2015/03/the-entropy-of-lego-durham-cathedral.html I was thinking about the number of ways that the molecules could be arranged as regards the cake. Beforehand I had separate piles of eggs, margarine, flour and sugar. Afterwards they were mixed and blended. the same molecules existed before and after. But beforehand they had to be in separate pile so the molecules were not interchangeable and there were fewer ways of swapping them around and still getting the same thing. The fewer the ways that molecules can be swapped to give you the same thing, the lower the entropy. So I'd argue that entropy does increase when you bake a cake and the Second Law of Thermodynamics is validated.

Stars in Swindon: diffraction spikes

I was at a christening in Swindon considering the stars at the feet of the Virgin. Stars are always drawn pointed although they are actually spherical balls of hot gas. The problem is diffraction when light enters your eyeball. It's all slightly problematic because the aperture is a circle so you should get concentric circle diffraction with a bright central bit called the Airy Disc. But a dilated pupil would have far too big a diameter to do this. Some sources suggest it is to do with surface tension and the liquid on the surface of the eyeball. A more understandable phenomenon is that of "diffraction spikes" forming spiked rays on photographs of stars through telescopes. The lines are produced by diffraction of light round the struts that hold up the secondary mirrors. http://en.wikipedia.org/wiki/Diffraction_spike