Problem to turn in on Thursday

Consider a Ferris wheel, radius 8-m. A 50-kg rider makes 2 rotations per minute. This rider (conveniently) is sitting on a scale.

What will the scale read at the top of the wheel?

What will the scale read at the bottom of the wheel?

How many rotations per minute must the wheel make so the the rider would feel weightless at the top ot the wheel?

Circular motion problems

1. Spinning bucket of water problem. Imagine a bucket of water (mass m) spun in a vertical circle with constant speed (v), if that were possible. What is the minimum speed such the water does NOT fall out of the bucket?

2. Consider a 'loop the loop' (radius r) Roller Coaster. What is the minimum speed for you to travel in a car so that you don't fall out of the roller coaster? Is this the same problem as above?

3. Now consider a roller coaster again - this time, imagine that you are going to the bottom of a curve (with constant radius, r). How does your 'apparent weight' (as measured by a scale that you are conveniently sitting on) vary with the speed of the roller coaster?

4. Consider a car rounding a curve (radius r) with coefficient of friction (u) between wheels and road. What is the relationship between v and u?

HW update

I don't have my text handy and can't post additional problems. However, I'll do so tomorrow - if you can solve them, please do so. If not, I'll understand. At the very least, make sure you're caught up with the older stuff.

hw

Chapter 6:

29

23

55

43

47

homework

Read chapter 6, particularly the sections on drag and circular motion.

There is no derivation for the drag relationship. Feel free to google it, though we will develop it in class.

Unrelated, but fairly awesome.

http://gizmodo.com/5850643/what-the-hell-magnets-why-are-you-so-amazing?tag=science

http://andrewsullivan.thedailybeast.com/2011/11/ment-5.html

You've seen the first already.

homework

Finish calculations for acceleration values (informal lab) and compare to experimental.

Try 2 more problems in chapter 5 (that's chapter FIVE.)

57, 59

Homework

Keep working through chapters 5 and 6. Read sample problem 5-4 carefully.

Try these problems in chapter 5:

51
55
65

Homework

Read chapter 5, or as much of it as you can. Try these problems: 13, 15, 19

FYI from class - just for fun

http://www.youtube.com/watch?v=oRLstHNRsdU

http://www.indiana.edu/~acoustic/s522/fourapdkp.html

Homework: I will place the take-home exam in your mailboxes and/or post it on this blog by Monday.

HW

Prep for a projectile lab on Friday. Have some type of protocol to measure the initial velocity and maximum height of air-powered rockets.

Hooray!

And the take-home test will be distributed on Friday. It will be due 2 classes later - there will be no other homework due during that time. Expect 4 problems: 1-D motion, vector problem (general), vector problem (i,j,k) and relativity.

Projectile HW

Chapter 4:

38
26
41
13

Don't forget the earlier vector problems.

Let's have a take-home test soon, covering one-dimensional motion, relativity and the intro to vectors (but not projectile motion).

hw for Friday

Chapter 3

27

31

37

42

71

On Friday, we will discuss motion in 2 dimensions - projectiles! Feel free to start reading chapter 4.

Thanks!

Vector HW

1. Consider a set of vectors:

A = 2i - 4j + 12k

B = 6i + 2j - 8k

Find the following:

A + B
B - A
the magnitude of each vector
the angle between the vectors

2. We didn't get into cross products seriously. Here's the brief definition: the cross product of 2 vectors is a third vector (perpendicular to the plane of the original 2 vectors; described by the right hand rule). The vector has magnitude given by:

A X B = A B sin(phi)

When you take the cross product of 2 vectors, you foil them (as we did for the dot product). However, doing the cross product of unit vectors (i, j, k) is trickier to determine. There is a simple way to remember this, but it's hard to describe in print - I'll show you Wednesday. Until then, here's the general answers:

i x j = k
j x k = i
k x i = j
i x k = -j
k x j = -i
j x i = -k

With this in mind, take the cross product of the two vectors above - the answer will be a vector (with i, j, and k components).

3. For fun:

If you understand the right hand rule, try these:

UP X WEST

BACKWARDS X DOWN

4. As always, be caught up on reading, etc.

vector notes 2

vector notes

Oh, and another thing....

To let you know where we're headed next.....

I'm thinking that another take-home quiz is in order - maybe next week?

I want to cover projectile motion - we didn't do it in great detail in 9th grade.

There will be a formal lab on projectiles.

After this, it's forces - this will have some of my "rocket science" ideas. I have parts for you to build your own model rockets (either alone or in pairs, as you wish). I'd like us to investigate the air resistance associated with high-speed flight.

If you have time, investigate ways to build a small wind tunnel. We may want to use this as a class.

Thanks!

Vector HW

Hi there!

I'd like you to prep for Monday's class by reading the chapter on vectors. Focus on the following:

vector magnitude
i, j, k components
vector multiplication
dot and cross products

I'd assign a couple of vector addition problems at this point, but I suspect that yesterday's stuff isn't too challenging yet. If you like, create a triangle (knowing 3 side, or 2 sides and the angle between) and use the laws of signs and cosines to determine the other information. Alternately, create your own river or plane problem to solve. Again - do this if it is helpful. It is more important to prep for Monday's class by learning about i, j, and k components

Grazie!

Homework

Nothing new

Just get caught up with the applets, etc.

Relativity fun!

Applets worth your time:

http://chair.pa.msu.edu/applets/travel/a.htm

http://www.its.caltech.edu/~phys1/java/phys1/Einstein/Einstein.html

https://parkscience.pbworks.com/w/page/43576403/Modern%20Physics%202011
See the video.

http://physics.ucsc.edu/~snof/Tutorial/index.html
Work through the tutorial, if you like.

http://www.kcvs.ca/site/projects/specialRelativity.html

http://physics.ucsc.edu/~snof/Rally/index.html
http://physics.ucsc.edu/~snof/Game/index.html
Games?

Relavitity problems

1. What are the Lorenz factors for velocity values of:
a. 0.1 c
b. 0.9 c
c. 0.99 c

2. Consider two twins, Spacey and Stacey. Spacey travels at 0.9 c to a planet (Planet Lally!) that is (measured before travel) 6 LY (light-years, or c-years) away. Stacey stays home. Spacey travels to the planet and quickly turns around once arriving. Find the following:
a. how much Stacey ages during the trip
b. how much Spacey ages during the trip
c. the odometer reading on Spacey's spaceship upon arriving at Planet Lally

3. In the problem above, the spaceship is measured to be 100-m long before flight. How long does it appear to:
a. those aboard it
b. those viewing it from Earth

4. Consider a group of pi-mesons (pions) traveling at 0.8 c. In the lab, the lifetime is measured to be 3 x 10^-8 seconds with no travel. How "old" can the pions become traveling at 0.8 c? How long a distance could they traverse?

Special relativity notes

more Einstein reading

http://en.wikipedia.org/wiki/Special_relativity

Read up until this part:

Reference frames, coordinates and the Lorentz transformation

Einstein redux

Apparently the recent link did not work - thanks, Jeremy. Try reading this:

http://www.pitt.edu/~jdnorton/Goodies/Einstein_and_S/index.html

How Einstein Changed the Way We Think About Science

John D. Norton
Department of History and Philosophy of Science, University of Pittsburgh
Pittsburgh PA 15260. Homepage: www.pitt.edu/~jdnorton
This page is available at www.pitt.edu/~jdnorton/goodies

This is an expanded version of my "What Is Einstein's Legacy to Me? Philosophy of Science" appearing in Imagine (Johns Hopkins Center for Talented Youth) Vol. 13, Issue 1, September/October, 2005.



We all know of Einstein's contribution to modern physics. Through his theories of relativity he showed us that there is a fastest possible speed and that light moves at it. He showed us that gravity is a curvature of spacetime. And he laid the foundations of modern quantum mechanics when he proposed that light really comes in little bundles of energy he called quanta. Any philosopher of science interested in the nature of space, time and matter has to take notice, for our accounts of all three were changed fundamentally by Einstein's hand.

What is less well recognized is how Einstein's work altered our understanding of the nature of science itself. To begin, he changed our ideas of how to do theoretical science. In 1905, he showed us how to make sense of the odd fact that light always propagates at exactly the same speed c, no matter how fast we go. The trick was to see that when we change our state of motion, we change our judgments of which events are simultaneous. His lucid analysis, laid out in the opening pages of his famous 1905 special relativity paper, was especially vivid. He used a thought experiment, in which asked us to imagine two clocks exchanging light signals and observers in different states of motion. The signals bounce, the clocks tick and altogether too quickly the final, astonishing result emerges.

The apparent ease with which ordinary thought experiments could yield extraordinary results was inspiring. It led many to try to copy his method They sought new theories, not in novel experiments, but in astonishing revisions of familiar notions like space and time, through carefully crafted thought experiments. These efforts rarely succeeded for those who are not Einsteins.

Another notion was read from Einstein's analysis of 1905. It was a view of which concepts may be used in science. They must be defined by the operations needed to measure the concept. So we can only use the concept of the simultaneity of two events if we can specify just how we may determine their simultaneity, by, for example, operations with light signals. This stringent demand is very effective if our goal is to force critical re-evaluation of some dubious concept. However it is as likely to cause problems where there should be none, for few of our concepts really conform to its standards.

Einstein invented neither the notion of the thought experiment nor the operational definition of a concept. He merely used them more perfectly than any who had gone before him.

The most enduring change brought by Einstein's work was to shake our sense of certainty. When Einstein entered science at the start of the 20th century, there was a strong sense of its stability. In antiquity, Euclid had described perfectly how space really is. In the 17th century, Newton had discovered the dynamics that govern time and matter. It is only from the perspective of this certainty that we can now understand the project of the influential eighteenth century philosopher Immanuel Kant. He felt compelled to devise an explanation of why all our experience must conform to the geometry of Euclid and the mechanics of Newton. The project now seems misplaced. Einstein showed us that both theories can fail when we enter the realms of the cosmically large, the very heavy, the atomically small and the very fast.

Einstein was not the only one to show us the fragility of our knowledge. But he was the first, the most effective, and the best remembered. He showed us that the old certainties had failed. So, we concluded, surely anything that replaces them could fail again.

The old confidence in our knowledge was based on the notion that experiment and experience could bear quite directly on our science. Some, like Ernst Mach, thought that all of science was or should be nothing more than compact summaries of experience. While this idea was always somewhat dubious, it could survive because even the most complicated theory of the era, Maxwell's electrodynamics, appeared to remain close to experience. For each of Maxwell's equations, one could point to experiments that seemed to be expressed just by that equation.

This sense of the closeness of theory to experience was shattered by Einstein's general theory of relativity. It required a new and complicated mathematics then unfamiliar to most physicists. Yet most of its predictions were no different than those of Newton's much simpler theory. If theories were merely summaries of experience and did not add to them, how could two theories, so much in agreement on experience, differ so much in structure?

Einstein's physics and the new physics developed by others in the twentieth century led to a sense of the fragility of theories and the powerlessness of evidence to pick out the unique truths of nature. Philosophers of science struggled to accommodate this new sense within their systems, all the while seeking to fit their ideas with Einstein's theories.

Einstein's own diagnosis of this gap between experience and theory was extreme. He proclaimed that concepts and theories are "free inventions of the human spirit" and that no method could assuredly take us from experience to the true theory. Here he contradicted the optimism of the nineteenth century during which many felt that scientific discovery could be reduced to simple recipes. John Stuart Mill continued a tradition extending back to the seventeenth century Francis Bacon. To identify the cause of some effect, he believed, one merely needed to collect cases in which the effect was present and those in which it was not. The cause could then be read directly from the systematic differences between the cases.

Later in life, Einstein came to a radical solution of the problem of responsibly practicing science while still believing that its core concepts are free inventions. Drawing on his discovery of general relativity, he concluded that the right concepts and theories could be found merely by seeking the mathematically simplest theories.

In my view, Einstein's response was too optimistic in his confidence that mathematical simplicity could be the guide to the truths of nature. Einstein was able to make no major discovery using this principle during the decades of his legendary and ultimately barren search for a unified field theory.

And Einstein's notion that concepts and theories are free inventions not fixed by experience seems too pessimistic, for science seems time and again to be able to determine the right theory on the basis of evidence. In the face of this commonplace of science, Einstein too seems to have had some difficulty maintaining his notion of free invention. He likened nature to a "well-designed word puzzle." While we may try to solve it with many words, only one "really solves the puzzle in all its parts."

This last view seems to me to capture much better the real power of evidence to point to a definite theory. If the equivalence of energy and matter expressed by E=mc2 is based on free inventions, why is there no alternative that enjoys equally powerful support from our experiences and experiments?



Some Reading

Einstein, Albert. Relativity: The Special and the General Theory. Methuen & Co., 1920.

Einstein, Albert. Ideas and Opinions. New York: Bonanza Books, 1954.

Howard, Don A., "Einstein's Philosophy of Science", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.) http://plato.stanford.edu/archives/spr2004/entries/einstein-philscience/.


John D. Norton is a licensed and certified dilettante whose hobby is the study of Einstein's work and thought. This hobby has so overtaken his life that he has little time for anything else and is Professor of History and Philosophy of Science and (Sept. 2005-) Director of the Center for Philosophy of Science at the University of Pittsburgh.

Copyright John D. Norton, May 14, 2005.

>

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/index.html

>

http://plato.stanford.edu/archives/spr2004/entries/einstein-philscience

Einstein!

Einstein notes

Worth a read (from an Einstein scholar and former prof of mine):

http://www.pitt.edu/~jdnorton/Goodies/Einstein_and_S/index.html

Notes from class:

And then there was Einstein…

Albert Einstein 1879-1955

http://www.aip.org/history/einstein/index.html

What’s happening around the turn of the 20th century? Physics was set to explode with 30 brilliant years of excitement and unprecedented activity

X-rays – Roentgen

Radioactivity – Becquerel, Marie & Pierre Curie

Blackbody radiation (and the quantum discontinuity) – Planck

1905/6 – Einstein publishes 6 major papers:

a) “On the electrodynamics of moving bodies”

b) “Does the inertia of a body depend upon its energy content?”

c) “On a heuristic point of view about the creation and conversion of light”

d) “On the theory of the Brownian movement”

e) “On the movement of small particles suspended in stationary liquid demanded by the molecular-kinetic theory of heat”

f) “A new determination of molecular dimensions”

What are these about anyway?

a. Special relativity (SR)

b. E = m c2 (actually, L = m c2)

c. Photoelectric effect, light quanta, fluorescence

d. Same as title

e. Brownian motion agan

f. Avagadro’s number, etc.

Now, these are interesting (and very different fields of study), but is this why we revere Uncle Al? Not necessarily. Others (Poincare, Lorentz) were working on what would become SR. Planck had introduced the quantum discontinuity (E = h f) and quantum mechanics (QM) would have many contributors. The photoelectric effect had also several investigators (Lenard, et.al.).

Mostly, Einstein’s legend grows because of General Relativity (GR), which appears 1912-1915 and later and on which he worked largely alone with pad and pen. He forced us to re-examine how we see ourselves in the universe; indeed, how we think of gravitation. All of this around the time his marriage was falling apart (he married young after fathering 1 illegitimate child) and he began an affair with his cousin (whom he would later marry). Also, between 1902 and 1909, Einstein held a modest post in Bern, Switzerland as a Patent Clerk. By 1914, he would be director of the Kaiser Wilhelm Institute (later Max Planck Institute).

Special Relativity

Spaceship – Inside an inertial reference frame (constant velocity), you can’t tell whether or not you’re moving (“Principle of Relativity”)

Biographical notes

1879 – born in Ulm, Germany

1884 – receives first compass

1895 – attempts to gain entrance to Swiss Polytechnic (and finish high school early), but is rejected

1896 – begins Federal Polytechnic (ETH) in Zurich, Switzerland

1898 – meets Mileva Maric

1900 – graduates from ETH

1901 – Einstein becomes Swiss citizen and moves to Bern; Mileva becomes pregnant

1902 – Lieserl born (put up for adoption); Hermann dies

1903 – Albert and Mileva marry

1904 – Hans Albert born

1905 – Einstein’s “Annus Mirabilus”, his miracle year; Ph.D. (Zurich)

1919 – divorces Mileva (having lived apart for 5 years); marries Elsa; GR verified

1921 – awarded the Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

1933 – settles in Princeton, NJ

1936 – Elsa dies

1939 – E. writes FDR

1940 – E. becomes American citizen

1949 – Mileva dies

1955 – E. dies

http://www.aip.org/history/einstein/index.html

http://www.albert-einstein.org/

http://einstein.stanford.edu/

http://en.wikipedia.org/wiki/Einstein

General Relativity

By 1907, E. wanted to advance the SR theory to include non-inertial (accelerated) frames of reference. Around this time, E. has the “happiest thought of my life”. In a uniformly accelerated spaceship, a stationary thing (ball, etc.) would appear to be falling (accelerating) down – it would be indistinguishable from normally accelerated motion. Light, too, follows this idea. Two clocks at different ends of an accelerated spaceship would be out of sync. Gravity is the result of the curvature of space and time?

Why does the Earth follow the Sun? Gravity – the very presence of the Sun causes Earth to veer from its otherwise straight (Newtonian inertial) path. With the Sun, it takes an elliptical path as its natural motion. Getting to this point, and showing that mass alters space and time is the real genius.

There is a breakdown of the observed geometry (Euclidean). E. must use non-Euclidean geometry (Gauss, surfaces, infinitesimal geometry) to consider the behavior of things (rods, etc.) on surfaces. He also considers the shortest distance between 2 points on a sphere (geodesic, great circle). He obtains the mathematical advice of his friend Marcel Grossman and studies (at great length) tensor calculus, differential geometry, Riemann and Minkowski math … it’s all puzzle solving. Soon, the principle of equivalence emerges. Eventually, the gravitational field equations appear (to show how matter “produces” gravity. GR was mostly worked out by 1913

Take-home quiz

Physics with Calculus
Take-home quiz

1. Consider a toy rocket being launched from rest. The rocket has a 5-s period of acceleration, after which it has attained a velocity of 45 m/s upward. Find the following:
a. the acceleration of the rocket
b. the height the rocket has achieved by the end of 5 seconds
c. the maximum height the rocket will attain
d. the total time in air spent by the rocket by the time it lands back on the ground
e. 3 graphs of motion that depict the entire flight of the rocket (x vs. t, v vs. t, a vs. t)


2. Consider a body that moves according to the following expression: x = 5t^2 – 10t + 4. Find the following:
a. expressions for velocity and acceleration
b. the time when the velocity becomes zero
c. the displacement after 30 seconds has passed

homework / Sep 26

Work on the formal lab, due Wednesday. If you want me to review a draft, leave it in my mailbox.

Also, discuss the problemset with classmates - try to get a sense of where your weaknesses are. I anticipate giving you a take-home quiz this Wednesday, to be due Monday.

Thanks!

The story of Schroedinger's Cat.

The story of Schroedinger's cat (an epic poem)

May 7, 1982
Dear Cecil:

Cecil, you're my final hope
Of finding out the true Straight Dope
For I have been reading of Schroedinger's cat
But none of my cats are at all like that.
This unusual animal (so it is said)
Is simultaneously live and dead!
What I don't understand is just why he
Can't be one or other, unquestionably.
My future now hangs in between eigenstates.
In one I'm enlightened, the other I ain't.
If you understand, Cecil, then show me the way
And rescue my psyche from quantum decay.
But if this queer thing has perplexed even you,
Then I will and won't see you in Schroedinger's zoo.

— Randy F., Chicago

Cecil replies:

Schroedinger, Erwin! Professor of physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don't worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
Win saw that the theory that Newton'd invented
By Einstein's discov'ries had been badly dented.
What now? wailed his colleagues. Said Erwin, "Don't panic,
No grease monkey I, but a quantum mechanic.
Consider electrons. Now, these teeny articles
Are sometimes like waves, and then sometimes like particles.
If that's not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
No sweat, though — my theory permits us to judge
Where some of 'em is and the rest of 'em was."
Not everyone bought this. It threatened to wreck
The comforting linkage of cause and effect.
E'en Einstein had doubts, and so Schroedinger tried
To tell him what quantum mechanics implied.
Said Win to Al, "Brother, suppose we've a cat,
And inside a tube we have put that cat at —
Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple mosquitoes
(Or something else rhyming) and, oh, if you got 'em,
One vial prussic acid, one decaying ottom
Or atom — whatever — but when it emits,
A trigger device blasts the vial into bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
The cylinder's sealed. The hour's passed away. Is
Our pussy still purring — or pushing up daisies?
Now, you'd say the cat either lives or it don't
But quantum mechanics is stubborn and won't.
Statistically speaking, the cat (goes the joke),
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous split,
But quantum mechanics must answer, "Tough shit.
We may not know much, but one thing's fo' sho':
There's things in the cosmos that we cannot know.
Shine light on electrons — you'll cause them to swerve.
The act of observing disturbs the observed —
Which ruins your test. But then if there's no testing
To see if a particle's moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability — certainty, never.'
The effect of this notion? I very much fear
'Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
"We've just flipped a coin and we've learned he's a corpse."'
So saith Herr Erwin. Quoth Albert, "You're nuts.
God doesn't play dice with the universe, putz.
I'll prove it!" he said, and the Lord knows he tried —
In vain — until fin'ly he more or less died.
Win spoke at the funeral: "Listen, dear friends,
Sweet Al was my buddy. I must make amends.
Though he doubted my theory, I'll say of this saint:
Ten-to-one he's in heaven — but five bucks says he ain't."

— Cecil Adams

http://www.straightdope.com/columns/read/113/the-story-of-schroedingers-cat-an-epic-poem

Chapter 2 problems worth a look

29, 31, 45, 47, 51, 57, 61, 89, 99, 101

Play around with these.

Class ideas

Based on today's conversation, here are some class ideas to consider for the year.

We'll do some traditional mechanics topics (1-d motion, 2-d motion, 3-d vectors, forces, energy, etc.)

Here are some other topics thrown about today:

Circuits 'n stuff
Fourier stuff
quantum mechanics
relativity
nuclear physics
sound
optics
lasers and holography

I like the idea of a mid-year project of your own choosing. Folks seemed semi-enthusiastic about that, so I suspect we'll try that. By then, I hope you'll have an idea of something you'd like to investigate on your own.

Welcome to Physics with Calculus! And thanks for such a pleasant first class.

SI units

SI Units

Howdy, and welcome to Physics!

Some comments on the first class. I speak about SI units at some length. To remind you:

Mass is measured based on a kilogram (kg) standard.
Length (or displacement or position) is based on a meter (m) standard.
Time is based on a second (s) standard.

How do we get these standards?

Length - meter (m)

- originally 1 ten-millionth the distance from north pole (of Earth) to equator
- then a distance between two fine lines engraved on a platinum-iridium bar
- (1960): 1,650,763.73 wavelengths of a particular orange-red light emitted by atoms of Kr-86 in a gas discharge tube
- (1983, current standard): the length of path traveled by light during a time interval of 1/299,792,458 seconds

That is, the speed of light is 299,792,458 m/s. This is the fastest speed that exists. Why this is is quite a subtle thing. Short answer: the only things that can travel that fast aren't "things" at all, but rather massless electromagnetic radiation. Low-mass things (particles) can travel in excess of 99% the speed of light.

Long answer: See relativity.

Time - second (s)

- Originally, the time for a pendulum (1-m long) to swing from one side of path to other
- Later, a fraction of mean solar day
- (1967): the time taken by 9,192,631,770 vibrations of a specific wavelength of light emitted by a cesium-133 atom

Mass - kilogram (kg)

- originally based on the mass of a cubic decimeter of water
- standard of mass is now the platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris
- secondary standards are based on this
- 1 u (atomic mass unit, or AMU) = 1.6605402 x 10^-27 kg
- so, the Carbon-12 atom is 12 u in mass

Volume - liter (l)

- volume occupied by a mass of 1 kg of pure water at certain conditions
- 1.000028 decimeters cubed
- ml is approximately 1 cc

Temperature - kelvin (K)

- 1/273.16 of the thermodynamic temperature of the triple point of water (1 K = 1 degree C)
- degrees C + 273.15
- 0 K = absolute zero

For further reading:

http://en.wikipedia.org/wiki/SI_units

http://en.wikipedia.org/wiki/Metric_system#History

>

In addition, we spoke about the spherocity of the Earth and how we know its size. I've written about this previously. Please see the blog entries below:

http://howdoweknowthat.blogspot.com/2009/07/how-do-we-know-that-earth-is-spherical.html

http://howdoweknowthat.blogspot.com/2009/07/so-how-big-is-earth.html


Physics - Yeah!!!