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: