# Physics Stop

## Torque equals rate of change of angular momentumMarcus WilsonMar 27

Another day, another New Zealand batting collapse.  But while Kane is still there, there’s hope.

Not what I wanted to blog about. Halogen lights. You know the ones, the little light bulbs that are all the fashion. You fit lots of them snuggly into your ceiling to provide a nice even illumination of the room without obtrusive cables and fittings hanging from the ceiling.

They are nasty things, for three reasons. First, they ain’t energy efficient. They might look hi-tec, but they rack up your electricity bill as fast as a few incandescent bulbs will – especially when you have lots of them.

Second, fitting snuggly into the ceiling means that you have further to reach to change them. Whereas I could do a hanging light fitting without even getting a chair (oh, the advantages of being tall) a chair is the minimum I need in our new house. For many of them, a step ladder is called for. Indeed, we have one light in the most stupidly located position imaginable. It is where the ceiling is the highest, on the upstairs landing right at the top of the stairs. To get to it, I need to put a step ladder at the top of the stairs and go to the top of the ladder and reach upwards. ACC would cringe at the prospect (and so do I). This light bulb is remaining unchanged.

And third, once you finally reach them, they are SO difficult to get in and out of the fitting. With a conventional bulb, you could grasp it and turn; but with this there is nowhere to grasp. To generate a torque on the bulb, which is what you need to do to turn it in the fitting, you need to use friction between your fingers and the bulb. But to stop your fingers sliding across the bulb, you need to press really hard. But also, because the bulb is small, you can generate very little torque. The torque, which is the total ‘strength’ of the turn, is given by the force you exert, times the radius of the circle that is being turned.  A small radius means that you need apply a lot of  force, which isn’t easy to do through friction alone. You can experience a similar thing with opening jam jars. There are a variety of inventions to cope with stiff lids – mostly they work by making the lid effectively bigger – e.g. by gripping the lid and providing you with something larger to turn. That means the radius of the turning circle is bigger, so the force you need to exert to give the same torque is lower.

A couple of days ago I changed a couple of bulbs in a friend’s house – he’s unable to do them himself. One of them, in particular, took an age to get out of the socket. I left with skin missing from my fingertips, because of the friction involved. People with arthritis would have no chance.

I feel like I need to invent a device to grip these things and let you remove them more easily – unless of course someone’s already invented it.

## Impossible angular momentumMarcus WilsonMar 24

Remember many, many years ago the urban myth that it had been scientifically proven that bumble-bees couldn’t fly? Many people took that to mean that science was clearly bonkers, and good reason to ignore anything a scientist said. Unfortunate, when as a scientist you want to campaign on the fact that science is a useful and productive way of looking at the world.

I have my own version of the bumble-bee problem: physics proves that it is impossible for a child to ride a scooter. I’ve come to this conclusion after playing ‘asteroids’ with oncoming scooter-borne children while walking the last bit of the way to work in the morning.  (Incidentally, I’m amazed that schools allow children to bring scooters, skateboards and the like. Skateboards were most definitely banned at school when I was there – and scooters, thankfully, didn’t exist in great numbers.)

Anyway – the issue. As any cyclist knows, it is not easy to fall off a moving bike. The reason is the angular momentum of the wheels. A spinning wheel carries angular momentum. It is a directional quantity – a wheel that is oriented vertically (as it should be in a bicycle) has a different angular momentum to one spinning the same rate but oriented parallel to the ground (as in a  bike just about to hit the ground). The greater the rate of spinning, the greater the angular momentum of the wheel, so the greater the difference in the two scenarios.  To change the angular momentum requires a torque, or turning moment. This can be done by moving your body off-centre. But if you have a lot of angular momentum to change, you need to apply a huge torque, which means the faster the wheel is spinning the less easy it is to pull it from a vertical position to a horizontal position. In fact, leaning one way will result in the bike changing direction, rather than falling.

A year 12 or 13 physics student should be able to estimate the angular momentum of a bicycle wheel. A similar calculation will give the angular momentum of the scooter wheel.  For the scooter, the wheels are tiny, and much less massive. They carry much less angular momentum (I estimate maybe around a tenth at a similar ground-speed), and that means one should be able to flip them from vertical to horizontal with much less torque. It’s hard to see how anyone could stay upright on one.

However, kids are good at doing impossible things, so why would that bother them?

## A rant for Friday afternoonMarcus WilsonMar 23

Forget Marmageddon – the university is clearly facing staplageddon. And it has for at least the last seven years. Why don’t students own staplers? How am I meant to keep control of assignments that are handed in on loose sheets of paper that aren’t stapled together? Half of them only have the student’s name of the first sheet. All it takes is one staple. One, solitary staple.  Is it TOO much to ask?

I think I’ll carry a stapler with me at all times and charge a dollar a time. I’d make a fortune.

P.S.  For those that aren’t kiwi, Marmageddon is the name given to the Marmite crisis here – there is no Marmite in the shops. NO MARMITE!? How can anyone survive?

P.P.S. Sorry, students, for getting at you like this. But stapling your work together really does make it easier for me and it’s less likely that a section of your assignment will go missing.

## Techno-failureMarcus WilsonMar 21

I think it’s reasonable to say that technology (by which I mean computers, software, mobile phones, video projectors etc) has greatly changed the way that teaching is carried out. One even might say ‘revolutionized’, though that might be taking things too far, since the fundamental principles, such as linking assessment with what you want students to learn, hasn’t changed.

YouTube is a great help for a science teacher. When there’s a demonstration that you want the class to see, but is rather too time-consuming or expensive or dangerous for you to set up yourself, you can usually find it on YouTube, often with a great commentary attached. The same is true for animations. Often in physics we talk about things changing with time – and graphs go only so far in getting the message across. Seeing something change ‘for real’ in a video can be a great help to a student.

So, for this afternoon’s lecture on Electromagnetic Waves, I had some nice animations prepared to show the students. Alas, the data projector threw a wobbly. So I was back to ‘old technology’, namely a whiteboard and pen. I think I coped well with the situation, though the whiteboard afterwards looked something like an Andy Warhol – lines and symbols going everywhere, in three different colours.

I can of course put the links to the relevant videos onto our on-line learning environment, Moodle, and the students can have a look at them in their own time. Unfortunately, Moodle is not 100% trustworthy either – earlier this semester it became a victim of its own success and became overloaded with users, resulting in people like me being chucked out of it mid-lecture.

So, in summary, it’s always worth thinking about how to teach without all the latest techno-props. Often we need to.

## Dumping light into spaceMarcus WilsonMar 19

Actually, I’ve been thinking a bit more about the 200% efficient LED I described last time. Maybe it can be a  solution to global warming after all.

The LED converts heat to light. Now, if one were to direct the light upwards, through the atmosphere and into space, it would escape the earth. Sure, it would eventually be absorbed somewhere, and warm the universe (and thus not break the second law of thermodynamics) but that makes it someone (or some-alien) else’s problem, not ours. (Dump the waste someplace else -  A very human way of looking at things).

Recall that the greenhouse effect works because the visible light from the sun passes through the atmosphere more easily than the infra-red light radiated by the earth. The more carbon dioxide, water vapour and methane in the atmosphere, the less easily infra-red energy is lost. Thus the earth captures the energy that is incident on it, but minimizes the energy that it loses. The earth wears, in effect, a one-way blanket. Energy can come in, but not out.

If we convert this infra-red energy back into visible light, through one or more of these LED devices, we can send it back through the atmosphere and into space, thus circumventing the problem caused by the carbon dioxide in the atmosphere. It doesn’t get rid of the carbon dioxide, it just makes for a heat loss mechanism that is immune to the carbon dioxide.

So, imagine half the world’s land area covered in little LEDs, beaming light into space (but only on cloud-free days). Interspersed are a plethora of power stations providing a power source for the LEDs. Now that we’ve got round the greenhouse problem we can do that with coal-fired power stations.  Yay. The way of the future. Use all the energy we like, carbon dioxide doesn’t matter any more.

It might, of course, be simpler, cheaper and more sustainable to greatly reduce the amount of carbon dioxide we chuck into the atmosphere, but that would be too obvious a solution, wouldn’t it?

## A solution to the world’s energy problems?Marcus WilsonMar 15

A student of mine has drawn my attention to this article. (Full article in Physical Review Letters here, a more accessible summary of it in Physics World here.)  It describes a light emitting diode (LED) that has a greater than 100% efficiency at converting electrical power to light. That is, put 30 picowatts of electrical power in, and we can get 70 picowatts of light out – an efficiency of more than 200%.  For those that don’t know, ‘pico’ means ‘times ten to the power of minus twelve’, or ‘a millionth of a millionth’. A picowatt of power isn’t much.

Uhh? What happened to conservation of energy? How can you get more power out than you put in? No, this doesn’t violate the laws of physics. The point is that 30 picowatts of ELECTRICAL power input (not total power input)  goes in, 70 picowatts of light comes out. There must be another power source as well, to make up the missing 40 picowatts.

It’s heat, from the surroundings. The LED, when operating, is cooling its surroundings. So we have 30 pW of electrical power and 40 pW of heat energy going into the device, and 70 nW of light coming out. It does make sense. It’s like a mini heat-pump. The heat pump in your house takes energy from the air outside and pulls it into the house. To do this requires energy input from the electricity supply – but the total energy (heat) you get inside your house is greater than the energy put in from electricity, so we can say the pump is more than 100% efficient.

Does this mean that we have a wonderful new source of lighting that beats the ‘energy-saving’ fluorescent bulbs hands-down?  Well, if you had enough of them, maybe. However,  to get such an efficiency, the LEDs run at very small currents – if you turn up the current (and make them brighter) the LEDs efficiency drops. So we need a huge number of these things, running at small currents, to make up a significant light source. But, as the Physicsworld article explains, there may be other niche applications, such as communications, where one can needs less bright light sources than for lighting your office.

So what about using these devices to cool? With enough of them, couldn’t we cool the atmosphere and solve global warming? Alas, no. The devices are producing radiation in the form of light, and this can be considered a form of heat. When the light strikes something and is absorbed, it heats up what is doing the absorbing. The obvious example is sunlight heating the earth’s surface. So, for 30 pW extracted from the local region, we get 70 nW elsewhere. It doesn’t help.

Just possibly the device could be used as a fridge for something very, very small, giving localized cooling. But for violating the second law of thermodynamics, no.

## A Threshold ConceptMarcus WilsonMar 12

In recent years, science education has been taking note of the idea of ‘threshold concepts’. The idea came out of studies in how students learn economics by Erik Meyer and Ray Land, but has much wider application.

We’ve done a bit of study in this at Waikato, particularly for electronics – see for example Jonathan Scott and Ann Harlow  (N.B. Full references are listed at the end.)

The basic idea is that some concepts in a subject are by their nature exceedingly difficult to learn. That’s because they typically require a change in the way a student thinks about something. They’re not just another fact to remember, or another technique for solving a problem, but transform the whole approach a student will take to something. With a threshold concept, there’s no ‘going-back’; once you have grasped it, the way you do things will change. Since students typically build knowledge on the foundation of what they already understand (or believe they understand) fitting in something that involves a shift in their fundamental thinking isn’t easy. A threshold concept may need to be presented to students many times before it gets grasped. The first time students are presented with it, it is likely to result in a sea of perplexed faces.

It’s tricky to give an example of a threshold concept for a general audience, because many are very specific to a discipline. Thinking back to childhood, one might recognize an example in understanding where money comes from. A very young child doesn’t get it – money is simply something that comes from Mum’s purse that can be exchanged for useful stuff. When Mum says "No, we don’t  can’t afford it", the child is perplexed. "But there’s money in your purse", he thinks. "You can always go to the bank and get some more." At some point he learns that there isn’t an endless supply of it – it gets earned – even the stuff that comes from the ATM – and at that point his thinking about it changes.

I ran into a threshold concept in a lecture on Friday. This one pertains to units in physics. In particle physics, one often talks about the mass of elementary particles as being in the unit MeV/c2.   (N.B. It’s tricky to write equations in MoveableType – the ’2′ here means ‘squared’.) For example, the mass of an electron is 0.511 MeV/c2.

What does this mean? Well, MeV (mega electron volt, or a million electron volts) is a measure of energy. One electron volt is the energy that an electron acquires when it is accelerated through a potential difference of 1 volt. It’s equal to 1.6 times 10 to the power of -19 joules. Students don’t typically have a problem with this – it’s just another unit – in the same way one can measure speed in metres per second or kilometres an hour or miles per hour, one can measure energy in joules (the S.I. unit of energy) or electron volts, (or kcal for that matter).

Now, recall Einstein’s famous E=mc2 equation, relating the rest-mass energy E of a particle to its mass m. Divide both sides by c2, and we get E/c2 = m. That is, an energy divided by a velocity squared is a mass. Students are with me so far.

But now the threshold. I say we can write mass as so-many MeV/c2  (a MeV divided by the speed of light squared.)  This they don’t like. Why? Because it involves the speed-of-light as part of the unit. The trouble is grasping what MeV/c2 represents. It’s sort of an equation but not quite. I think the problem here lies with the fact that my students don’t fully understand units in general – they have the idea they are a tag-on at the end of a number, rather than something that is absolutely integral to the quantity itself. What’s curious was that if I wrote the mass of an electron as (0.511 MeV)/c2, they were happy. It’s an algebraic equation – take the 0.511 MeV, and divide it by the value for the speed of light squared. But shift the brackets to 0.511 (MeV/c2) and suddenly it’s a conceptual jump too far.

It certainly appears to be a threshold for them, and, according to the literature, I can’t expect them to grasp it quickly. Thinking back to my student days, I didn’t grasp it quickly, either.

References:

Land R, Cousin G, Meyer JHF and Davies P (2005). Threshold concepts and troublesome knowledge (3): Implications for course design and evaluation. In Rust C (ed.) Improving Student Learning – equality and diversity. Oxford: OCSLD.

Meyer JHF and Land R (2003). Threshold concepts and troublesome knowledge (I): linkages to ways of thinking and practising. In Rust C (ed.), Improving Student Learning – ten years on. Oxford:OCSLD.

Meyer JHF, Land R and Davies P (2006). Implications of threshold concepts for course desing and evalutation. In Meyer JHF and Land R (eds.) Overcoming Barriers to Student Understanding: threshold comcepts and troublesome knowledge. London and New York:Routledge.

Scott J, Harlow A, Peter M and Cowie B. (2010). Threshold Comcepts and Introductory Electronics. Proceedings of Australasian Association for Engineering Education, Sydney.

## PhysicsStop is five hundred!Marcus WilsonMar 10

1 Comment

This is the 500-th entry on PhysicsStop.

That’s something I didn’t expect when I started the blog three and a half years ago.

Next target is a thousand. That’s going to be some way off. Blogging might be defunct by the time I reach that! – or a sign that you’re an old person.

## Newton’s laws in actionMarcus WilsonMar 08

For reasons best known to their little chicken-brains, Hyacinth and Brigitta (our chickens) have decided that their coop is no-longer the des-res that it once was and a far better location for a night in the wind and rain is on top of the garden shed. The problem is that neither (especially Brigitta) is particularly proficient at flying yet, so getting on top of the shed is right at the limit of their abilities.

Watching them in the evening is hilarious. They strut around the base of the shed, looking very agitated (probably because they’ve got an audience of me, Karen and the cat), trying to locate the best launching spot. Despite being the least able, it’s Brigitta that always goes first. She’ll crouch, then spring into the air – then out come the wings and its manic flapping and squarking all the way to the roof of the shed. If she misjudges it, she’s left grabbing at the grape vine and runner beans that climb up the side of the shed, and she hauls her way the final few centimetres to the top.

Once Brigitta’s settled down, Hyacinth has a go, usually rather more safely, but still far from elegantly.

While their abilities in locating safe, quality housing are somewhat questionable, their understanding of Newtonian mechanics is impeccable. To reach the top of the shed, they need to do work against the force of gravity. This is first done by the initial jump – they give themselves initial kinetic energy by pushing from the ground. By Newton’s third law, as they push downwards, the ground pushes back at them, and they are propelled upwards. The greater the velocity obtained in the initial jump, the more likely they are to be successful.

The next stage is the flap. Here they are using their wings to provide an upward force, in opposition to the downward force provided by gravity. Force is the rate of change of momentum. To provide a force now, they are propelling air downwards, rather like a helicopter does.  The more downward momentum they can give to the air, the correspondingly greater the upward force they are going to experience, and, again, the greater their chances of making the roof.

I don’t think even Hyacinth is yet capable of generating enough upward force with her wings to balance the force of gravity. That means that, while she is in the air, her net acceleration is downwards. If she’s moving upwards, because of the initial jump, she will find that her upward velocity reduces. If she didn’t land on the shed, but kept flapping, eventually that upward velocity would drop to zero, then it would become a net downward velocity, and she’ll land on the ground again. That means there’s a limit to how high she can get.

Evidence for this comes from watching them get down from the shed in the morning. Again, its frantic flapping as they try to control the speed of their descent. Both end up hitting the ground harder than I’m sure they’d like to. Even still, it’s the shed that gets their vote for a wet and windy night. Strange things.

## Putting your life into perspectiveMarcus WilsonMar 06

I came across these blog entries from David Spiegelhalter at the weekend from a statistician. In his posts he talks about quantifiying the risk from various activities (even just living) using the terminology of the ‘microlife‘ and the ‘micromort‘.

The microlife is defined as 30 minutes – very approximately a millionth of the remaining life expectancy of a young adult.  I’m only a couple of sentences into this blog post and I’ve already spent a tenth of a microlife writing them! So just living for 30 minutes will take a microlife from you, but there are ways of rattling through them more quickly – e.g. smoking (half a microlife a cigarette) and eating unhealthily. However, it’s not all bad news; Spiegelhalter explains that we actually gain  bonus microlifes each day simply due to ongoing improvements in medical science. Once you’ve spent about a million microlives, you die. On average, of course. Isn’t it nice to be reminded that you’re hurtling forward in time towards your death?

The micromort is a bit easier to define – being a one-in-a-million chance of death due to some prescribed activity. So a parachute jump, according to the blog,  is a 10 micromort activity (each jump gives a one in one-hundred thousand chance of death), which is quite low. Similar to driving 4000 km in a car in the UK. Climbing Mt Everest is an eye-watering 40,000 micromort activity (or 40 millimorts, I suppose).

I have previously talked about the risks from exposure to radiation. What matters in terms of risk is the effective dose equivalent, that you receive. The information I have available quickly to hand, gives a rough risk factor of 1 in 60 chance (i.e. about 17000 micromorts) of something really nasty happening to you per sievert of effective dose equivalent. The dose equivalent you get from background radiation (and this varies hugely depending on where exactly you live) is typically of order 2  millisieverts per year, i.e. giving about 30 micromorts per year. That’s three parachute jumps, or 12000 km driving. Not something to worry much about from day to day,

Anyway, have a read of the articles, they are quite amusing and rather frightening. In this time taken to write this post a microlife has vanished from my account, so it is time I did something rather more productive.

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