Friday, August 31, 2007

The Dome: A Simple Violation of Determinism in Newtonian Mechanics

- John D. Norton
Department of History and Philosophy of Science, University of Pittsburgh

The law of conservation of energy can be related to work done. See Chapter 13 of Feynman Lectures vol 1, entitled "Work and Potential Energy".

Thursday, August 30, 2007

The sum of all external forces equals the rate of change of the total momentum of all particles inside.

- Richard P. Feynman
The Feynman Lectures, vol 1 p. 10.3
first published 1963

All of our ideas in physics require a certain amount of common sense in their application; they are not purely mathematical or abstract ideas. We have to understand what we mean when we say the phenomena are the same when we move the apparatus to a new position. We mean that we move everything that we believe is relevant; if the phenomenon is not the same, we suggest that something relevant has not been moved, and we proceed to look for it. If we never find it, then we claim that the laws of physics do not have this symmetry.

- vol 1 p. 11.1

The rate of change of kinetic energy of an object is equal to the power expended by the forces acting on it. d(KE)/dt = F.v

Then, d(KE) = F.ds (since v = ds/dt).
Integrate, delta KE = integral point 1 to point 2 (F.ds)
This is the work done by the force on the object. F, v, and s are vector quantities, by the way.

As can be seen, power = work done per unit time.

- derivation is from vol 1 p. 13.2-13.3

Monday, August 27, 2007

Relaxation: a state of deep rest in which the metabolism of the body slows; less oxygen is needed, the heart and respiration rates drop, blood pressure drops, and brain waves slow to an alpha state.

(the state I'm in at 8pm each day, haha)

Friday, August 24, 2007

9-4 What is the force?

In order to use Newton's laws, we have to have some formula for the force; these laws say pay attention to the forces. If an object is accelerating, some agency is at work; find it. Our program for the future of dynamics must be to find the laws for the force.

- Richard P. Feynman
The Feynman Lectures, vol 1 p. 9.3
first published 1963

Wednesday, August 22, 2007

The language of probability allows us to speak quantitatively about some situation which may be highly variable, but which does have some consistent average behaviour.

- Richard P. Feynman
The Feynman Lectures, vol 1 p. 6.1
first published 1963

Tuesday, August 14, 2007

Frankly, I am so tired now that I could weep. Consider this a case of temporary insanity.

Monday, August 13, 2007

Re the July 20 entry, something has come out of the hard work.

The next step, now.

I've been very busy since mid-June, this looks set to continue. Apologies for the nonsense posted since then.

Monday, August 06, 2007

How can you be anything other than yourself, a friend asked.

When the circumstances call upon you to do thus, I said in reply.

When is that, she said.

When you feel you have to, and you choose to do so, I said.

Those two are not the same, she said.

Yes, indeed, I said.

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