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PHYSICS 104: Uncertainty and Chance in Physics
Prof. S. Teitel stte@pas.rochester.edu ----- Fall 2000

 Friday, December 15, 2000

In responce to an email from one member of the class, I replied with the message below. I post it here for you all to read. I hope it gives you some indication of what I think the basic formulas are that you should know for the exam.

-- S. Teitel

```=================================================================
Sitting here thinking, the "new" formulas since exam I
that come to my mind are:

** Random walk (both unbiased and biased):

1) average distance in N steps:   mu_N = N * mu_1

2) standard deviation of distance in N steps: sigma_N = sqrt(N) * sigma_1

You should be able to compute mu_1 and sigma_1 just by
applying the basic definitions of average and standard deviation
to the distance traveled in one step, rather than by memorizing
the any particular formulars.  For a walk in which the steps
are +L with prob p, and -L with prob 1-p,

mu_1 = (L) * (p) +  (-L) * (1-p)
(sigma_1)^2 = (L)^2 * (p) + (-L)^2 * (1-p) - (mu_1)^2

For a random walk defined by another one-step process, these
might be something else.
You should understand where the above come from, so you can
derive them, rather than memorize them.  In fact, (1) and (2)
above are just the same results as used in many other places
for Exam I, so they really shouldn't count as new equations you
need to learn for exam II.

** Diffusion:

If the number of steps is proportional to time, N = t/tau
(tau is time per step), then the diffusion constant D is
defined by

3) (sigma_N)^2 = D * t

from this and the above you should then be able to derive
D = (sigma_1)^2/tau

The drift velocity u is defined by

4) mu_N = u * t

so you should be able to derive
u = mu_1/tau

** Newtonian Mechanics:

Know what a vector is and how to add and subtract them.

5) velocity:  v = (Delta x)/(Delta t) as (Delta t )--> 0

6) acceleration:  a = (Delta v)/(Delta t) as (Delta t )--> 0

uniform circular motion, where r=radius, tau=period:

7) speed: v = 2 * pi * r/tau  velocity directed tangential to motion

8) centripetal acceleration  a = v^2/r  directed radially inwards

combining the two above gives a = (2 * pi / tau)^2 * r
so this is not an additional one to memorize - know how
to derive it.

9) Newton's 2nd Law:  F = m * a

Gravitation

10) at surface of earth: F_grav = m * g

11) in general:  F_grav = G * m_1 * m_2 / r_12

From the above you should be able to derive (not memorize)
things like Kepler's law, speed of an object in orbit, how
g is related to G, etc.

** Energy:

12) kinetic energy:  E_kinetic = (1/2) * m * v^2

13) gravitational potential energy: E_potential = m * g * h

14) conservation of energy:  E_total = E_kinetic + E_potential
has the same value at all times during an objects motion

** Gases:

Understand the concepts of atomic mass unit (amu), mole,

15) Ideal gas law:  P * V = N * k_B * T

or  P * V = n * R * T  where R = N_A * k_B

16) kinetic theory of gases: E_kinetic = (3/2) * k_B * T
is kinetic energy of one molecule in an ideal gas at temperature T.

I cannot guarentee that I haven't missed one, but it seems
to me that the above are the important equations to know.
Everything else is in understanding the concepts behind
these equations, and in knowing how to apply them.  I do not
expect you to memorize the numerical values of physical constants.

The text has several worked out problems in chapters 6 and 7
(Newtonian Mechanics, and Gases).  You could check these if
you want to see sample problems (note, we did not cover chapter
5, so you dont need to know what is in it).
```

 Tuesday, December 12, 2000

EXAM 2

Wednesday December 20, 4pm, B&L 405

 Wednesday, November 29, 2000

### Important Notice

As discussed in yesterday's lecture, the grading scheme for the course has been modified as follows:

 Homework 40% Exam 1 30% Exam 2 30%

Exam 2 will cover only material since Exam 1, i.e. from random walks and diffusion, through the end of the semester. Note however that since the material in this course builds on itself, concepts from this second half of the course may involve concepts and results from the first half of the course, and these may therefore appear in the problems in Exam 2.

Exam 2 will take place during the time period scheduled for the final exam, December 20, 4pm, in B&L 405. Exam 2 will last one and a half hours.

 Wednesday, November 1, 2000

The first inclass exam has been scheduled for Tuesday November 14, 2pm, in lecture at the usual time and place. The exam is closed book, closed notes, and covers material through problem set 6, i.e. through the normal distribution. Be sure to bring a calculator.

Solutions to problem set 6 have been posted.

 Wednesday, October 25, 2000

Lecture this Thursday Oct. 26 is cancelled.

Homework 6 will therefore be due in lecture Tuesday Oct. 31.

 Thursday, October 19, 2000

Solutions to Homework Sets 4 and 5 are now posted

Homework 6 is posted and is due Thurs. Oct 26.

 Friday, October 6, 2000

I have posted a new Homework Set 5. These problems are meant to be similar to the first three problems that were on Set 3, to give you more practice on these types of questions. These will be due Tues. Oct. 17. If you find yourself getting stuck, please come to see me for help. These are the sort of problems that I would like you all to be able to do.

 Wednesday, October 4, 2000

Homework Set 4 is due Thursday October 12.

Do NOT do problem (1). You only have to do problem (2); but do it well! Come to me for help if you need it.

 Monday, September 25, 2000

The Class Notes and Homework pages are now up-to-date!

 Monday, May 15, 2000

This is the home page for Physics 104, Uncertainty and Chance in Physics. I will use this page for posting announcements to the class throughout the semester.

The links on the left had side take you to various information pages for the course. These pages are still under development.

For a description of the course and tentative syllabus, see the course Announcement.

-- S. Teitel

Last update: Tuesday, August 14, 2007 at 2:31:39 PM.