Physics Olympiad Preparation Books:
"An Introduction to Mechanics" by Kleppner and Kolenkow "Classical Mechanics" by John R. Taylor "Introduction to Classical Mechanics with Problems and Solutions" by David Morin "Classical Dynamics of Particles and Systems" by Jerry B. Marion and Stephen T. Thornton "Special Relativity" by A.P. French "Vibrations and Waves" by A.P. French "Introduction to Electrodynamics, 3rd ed." by David J. Griffiths "Electricity and Magnetism" by Edward M. Purcell "Electromagnetic Fields and Waves" by Paul Lorrain and Dale Corson
Physics LimericksFor your viewing pleasure, and perhaps for your educational pleasure, I've included some physics limericks here. Some are funny. Some are stupid. But at least they are all physically accurate (give or take). Many of them can be found scattered throughout the textbook for the Physics-16 course here at Harvard. (Some more physics humor is located here.) David Morin
No pain, no gain. Alas, there are no shortcuts to learning physics... The ad said, for one little fee, You can skip all that course-work ennui. So send your tuition, For boundless fruition! Get your mail-order physics degree!
Always check your units! Your units are wrong! cried the teacher. Your church weighs six joules what a feature! And the people inside Are four hours wide, And eight gauss away from the preacher!
And check the limiting cases, too! The lemmings get set for their race. With one step and two steps they pace. They take three and four, And then head on for more, Without checking the limiting case.
When converting the units of a quantity, all you have to do is multiply by 1 in an appropriately chosen form. For example, in converting minutes to seconds, just multiply 1min by 60s/1min (which equals 1), to obtain 1min=(1min)(60s/1min)=60s. The minutes cancel, and you're left with seconds. Of course, you could also multiply by 1 in the form of (1min/60s) to obtain 1min=(1min)(1min/60s)=1min2/60s. This does indeed equal 1 minute, but no one would know what you were talking about if you said you could run a 1min2/10s mile.To figure the inches youve run, Or to find the slug mass of the sun, Forget your aversion To unit conversion. Just multiply (wisely!) by 1.
People tend to rely a bit too much on computers and calculators nowadays, without pausing to think about what is actually going on in a problem. The skill to do math on a page Has declined to the point of outrage. Equations quadratica Are solved on Math'matica, And on birthdays we don't know our age.
Enrico Fermi was known for his ability to estimate things quickly and produce an orderof-magnitude guess with only minimal calculation. Hence, a problem where the goal is to simply obtain the nearest power-of-10 estimate is known as a "Fermi problem". Of course, sometimes in life you need to know things to better accuracy than the nearest power of 10...How Fermi could estimate things! Like the well-known Olympic ten rings, And the one-hundred states, And weeks with ten dates, And birds that all fly with one... wings.
Newton's first law, "A body moves with constant velocity (which may be zero) unless acted on by a force," appears at first glance to be rather vacuous. In the words of Sir Arthur Stanley Eddington, it says that "every particle continues in its state of rest or uniform motion in a straight line except insofar that it doesn't." But the first law actually does have some content. In particular, it gives a definition of an "inertial frame" (which is defined to be one in which the first law holds). This inertial frame is then used as the setting for Newton's second law.
For things moving free or at rest, Observe what the first law does best. It defines a key frame, Inertial by name, Where the second law then is expressed.
Atwood's machines can be pretty hairy. But no matter how complicated they get, there are only two things you need to do to solve them: (1) Write down the F=ma equations for all the masses (which may involve relating the tensions in various strings), and (2) relate the accelerations of the masses, using the fact that the lengths of the various strings don't change (also known as "conservation of string"). It may seem, with the angst it can bring, That an Atwood's machine's a harsh thing. But you just need to say That F is ma, And use conservation of string!
Galileo's experiment worked because the air is sufficiently thin. Who knows what he would have concluded if we lived in a thicker medium... What would you have thought, Galileo, If instead you dropped cows and did say, "Oh! To lessen the sound Of the moos from the ground, They should fall not through air but through mayo!"
The classic example of the independence of the x- and y-motions in projective motion is the "hunter and monkey" problem. In it, a hunter aims an arrow at a monkey hanging from a branch in a tree. The monkey, thinking he's being clever, tries to avoid the arrow by letting go of the branch right when he sees the arrow released. The unfortunate consequence of this action is that he will get hit, because gravity acts on both him and the arrow in the same way; they both fall the same distance relative to where they would have been if there were no gravity. And the monkey would get hit in such a case, because the arrow is initially aimed at him. If a monkey lets go of a tree, The arrow will hit him, you see, Because both heights are pared By a half gt2 From what they would be with no g.
Induction is a wonderful tool, but it shouldn't be abused... "To three, five, and seven, assign A name," the prof said, "we'll define." But he botched the instruction With woeful induction, And told us the next prime was nine.
What really happened on that hill...
In Boston, lived Jack, as did Jill, Who gained mgh on a hill. In their liquid pursuit, Jill exclaimed with a hoot, " I think we've just climbed a landfill!" While noting, "Oh, this is just grand," Jack tripped on some trash in the sand. He changed his potential To kinetic, torrential, But not before grabbing Jill's hand.
Newton's law of gravitation holds over a vast range of distance scales. Apples, moons, and stars all behave in the same manner, dependent on the 1/r form of the gravitational potential. Newton said as he gazed off afar, "From here to the most distant star, These wond'rous ellipses And solar eclipses All come from a 1 over r."
The realization was nice, but then it took him another 20 years to develop calculus so that he could prove it mathematically. Newton looked at the data, numerical, And then observations, empirical. He said, "But, of course, We get the same force From a point mass and something that's spherical!"
Rockets make use of conservation of momentum, by ejecting small particles with very large speed. You never know when this technique might come in handy. Roger Clemens was stuck on a lake, With no wind, oars, or fuel big mistake! So he thought like a rocket, And emptied his pocket, And left all his change in his wake.
It's no coincidence that physicists study the harmonic-oscillator potential, kx2/2, so much. A quick application of the Taylor-series expansion shows that any potential looks basically like a quadratic, if you look at a small enough region around an equilibrium point. A potential may look quite erratic, And its study may seem problematic. But down near a min, You can say with a grin, "It behaves like a simple quadratic!"
Given a sufficiently long lever-arm, you can produce an arbitrarily large torque. This fact led a well-known mathematician from long ago to claim that he could move the earth if given a long enough lever-arm. One morning while eating my Wheaties, I felt the earth move 'neath my feeties. The cause for alarm Was a long lever-arm, At the end of which grinned Archimedes.
On a rotating platform, the Coriolis force always points in the same direction relative to the direction of motion. Whether it's to the left or to the right depends on the direction of rotation. But given w , you're stuck with one or the other. On a merry-go-round in the night, Coriolis was shaken with fright. Despite how he walked, 'Twas like he was stalked, By some fiend always pushing him right.
The kinetic energy of a body can be found by treating the body as a point mass located at the CM, and then adding on the kinetic energy of the body due to the motion relative to the CM. To calculate E, my dear class, Just add up two things, and you'll pass. Take the CM point's E, And then add on with glee, The E 'round the center of mass.
=dL/dt is valid only if the origin (the point around which and L are calculated) satisfies one of the following conditions: (1) The origin is the center of mass, (2) The origin is not accelerating, or (3) The acceleration the origin is parallel to the vector from the origin to the center of mass. This third condition is rarely invoked. So, when choosing an origin, just play it safe and heed the following... For conditions that number but three, We say, "Torque is dL by dt." But though they're all true, I'll stick to just two; It's CM's and fixed points for me.
If a force is always applied at the same position relative to the origin around which the angular momentum is calculated (as in the case for a quick blow to an object), then L is proportional to p, with the constant of proportionality being the leverarm of the force. Even if we don't know what L and p are, we know what their ratio is. What L was, he just couldn't tell. And p? He was clueless as well. But despite his distress, He wrote down the right guess For their quotient: the lever-arm's l.
When studying central forces, conservation of angular momentum is utilized to write the angular dependence in terms of the radius, thereby reducing the problem to an ordinary 1-