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Discovering Gravity
Michael Fowler 1/22/07
Terrestrial Gravity: Galileo Analyzes a Cannonball Trajectory
From the earliest times, gravity meant the tendency of most bodies to fall to earth. In contrast,
things that leaped upwards, like flames o
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A New Thermodynamic Variable: Entropy
Michael Fowler 7/10/08
Introduction
The word entropy is sometimes used in everyday life as a synonym for chaos, for example: the
entropy in my room increases as the semester goes on. But its also b
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The Doppler Effect
Michael Fowler 10/14/09
Introduction
(Flashlet here)
The Doppler effect is the perceived change in frequency of sound emitted by a source moving
relative to the observer: as a plane flies overhead, the note of the en
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Using Dimensions
Michael Fowler, UVa
Some of the most interesting results of hydrodynamics, such as the sixteen-fold increase in flow
down a pipe on doubling the radius, can actually be found without doing any calculations, just
from d
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Complex Numbers
Michael Fowler 2/15/07
Real Numbers
Let us think of the ordinary numbers as set out on a line which goes to infinity in both positive
and negative directions. We could start by taking a stretch of the line nea
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Heat Engines: the Carnot Cycle
Flashlet here!
Michael Fowler 7/3/08
The Ultimate in Fuel Efficiency
All standard heat engines (steam, gasoline, diesel) work by supplying heat to a gas, the
gas then expands in a cylinder and pushes a pi
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Brownian Motion
Michael Fowler, U. Va. 8/1/08
See Applet here!
Introduction: Jiggling Pollen Granules
In 1827 Robert Brown, a well-known botanist, was studying sexual relations of plants, and in
particular was interested in the particl
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Boyles Law and the Law of Atmospheres
Michael Fowler, UVa 6/14/06
Introduction
Weve discussed the concept of pressure in the previous lecture, introduced units of pressure
(Newtons per square meter, or Pascals, and the more familiar po
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Boundary Conditions: at the End of the String
Michael Fowler 3/12/07
Adding Opposite Pulses
Our first move in working with waves was to jiggle the end of a string (or spring) and generate a
pulse that we saw traveled along with no perc
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The Bernoulli Effect
Michael Fowler 6/12/06
Suppose air is being pumped down a smooth round tube, which has a constant diameter except
for a section in the middle where the tube narrows down to half the diameter, then widens out
again.
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Early Attempts to Understand the Nature of Heat
Michael Fowler, University of Virginia, 6/3/08
When Heat Flows, What, Exactly is Flowing?
By the late 1700s, the experiments of Fahrenheit, Black and others had established a systematic,
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From a Circling Complex Number to the Simple Harmonic
Oscillator
Michael Fowler
Describing Real Circling Motion in a Complex Way
Weve seen that any complex number can be written in the form z = rei , where r is the distance
from the or
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Visualizing Gravity: the Gravitational Field
Michael Fowler 2/14/06
Introduction
Lets begin with the definition of gravitational field:
The gravitational field at any point P in space is defined as the gravitational force felt by a tin
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Working with Gravity: Potential Energy
Michael Fowler 31/1/07
Gravitational Potential Energy near the Earth
We first briefly review the familiar subject of gravitational potential energy near the
Earths surface, such as in a room. The
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Elliptic Orbits: Paths to the Planets
Michael Fowler 1/23/07
Deriving Essential Properties of Elliptic Orbits
From a practical point of view, elliptical orbits are a lot more important than circular
orbits. A spaceship leaving earth an
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Binary Stars and Tidal Forces
Michael Fowler 1/29/07
Binary Stars
Up to this point, weve been considering gravitational attraction between pairs of objects where
one of them was much heavier than the other, and was taken to be fixed. T
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Remarks on General Relativity
Michael Fowler, University of Virginia
Einsteins Parable
In Einsteins little book Relativity: the Special and the General Theory, he introduces
general relativity with a parable. He imagines going into dee
Van der Waals Equation
1400
Michael Fowler, UVa
(P + a/V^2)(V - b) = RT
(for one mole)
80
70
60
50
600
1.382
0.03186
287
0.05
0.0005
Delta_T =
90
1000
800
Use the slidebar for T, put in other numbers by hand:
s ome given on second sheet.
T emperat ure
a=
Simple Pendulum Spreadsheet
Michael Fowler, University of Virginia
Link to lecture
Simple Pendulum
Click on and change the red numbers below!
(See Sheet 2 for a brief discussion of the construction of the table
below from the differential equation.)
L=
g=
Complex Plane Representation of the Simple Harmonic Oscillator
Michael Fowler
Animate by clicking and holding
on end of scrollbar
A=
1
delta=
0
omega_0=
2
omega=
2
b/2m =
0
t=
0.375
15
x
y
0
0
0.731689 0.681639
0.731689
0
0
0
-0.681639 0.731689
0
0
Aeiwt
Isotherms and Adiabats
Michael Fowler
Iso t herms PV = RT f or One Mole
gamma=
18
1.67
16
373
273
Adiabat_1=
Adiabat_2=
P r e s s u r e in At m o s p h e r e s
T_hot=
T_cold=
70
50
V_init=
delta_V=
2
0.04
14
12
10
8
6
4
2
0
1
2
3
4
5
6
Vo lume in Lit e rs
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Analyzing Waves on a String
Michael Fowler 5/30/08
From Newtons Laws to the Wave Equation
Everything there is to know about waves on a uniform string can be found by applying Newtons
Second Law, F = ma , to one tiny bit of the string.
Lectures on Oscillations and Waves
Michael Fowler, UVa, 6/6/07
FROM A CIRCLING COMPLEX NUMBER TO THE SIMPLE HARMONIC OSCILLATOR .3
Describing Real Circling Motion in a Complex Way.3
Follow the Shadow: Simple Harmonic Motion .4
OSCILLATIONS.5
Introduction.