3A Wave Motion I
1
Chapter 1
Reflection of Light
Reflection of Light
Practice 1.1 (p. 5)
1
C
2
C
3
(c)
Luminous objects: candle flame, lighted
lamps and the sun
Non-luminous objects: books, blackboards
and the moon
(Or other reasonable answers)
4
(a) Dive
Determine the moment produced by the force F in Fig. 4—14a about
point 0. Express the result as a Caltesian vector.
SOLUTION
As shown in Fig. 4—14a, either r A or ['3 can be used to determine the
moment about point 0.These position vectors are
rA = {12k}
At t = I], a wheel rotating about a fixed axis at a constant angular aeeeleration has an angular 1velocityr of 2.1]
radr's. Two seconds later it has turned through 5.13 complete revolutions. What is the angular acceleration
of this wheel?
a. 1? ranlfs2
h.
CHAPTER 14:
POLYMER STRUCTURES
ISSUES TO ADDRESS.
What are the basic microstructural features?
How are polymer properties effected by
molecular weight?
How do polymeric crystals accommodate the
polymer chain?
Chapter 14 - 1
Chapter 14 Polymers
What is
Chapter 12: Structures &
Properties of Ceramics
ISSUES TO ADDRESS.
Structures of ceramic materials:
How do they differ from those of metals?
Point defects:
How are they different from those in metals?
Impurities:
How are they accommodated in the lattic
Chapter 9: Phase Diagrams
ISSUES TO ADDRESS.
When we combine two elements.
what equilibrium state do we get?
In particular, if we specify.
-a composition (e.g., wt% Cu - wt% Ni), and
-a temperature (T )
then.
How many phases do we get?
What is the compo
Chapter 3: The Structure of Crystalline Solids
ISSUES TO ADDRESS.
How do atoms assemble into solid structures?
(for now, focus on metals)
How does the density of a material depend on
its structure?
When do material properties vary with the
sample (i.e.
Chapter 5: Diffusion in Solids
ISSUES TO ADDRESS.
How does diffusion occur?
Why is it an important part of processing?
How can the rate of diffusion be predicted for
some simple cases?
How does diffusion depend on structure
and temperature?
Chapter 5
Dynamics and Relativity: Example Sheet 3
Professor David Tong, February 2014
1. In a system of particles, the ith particle has mass mi and position vector xi with
respect to a xed origin. The centre of mass of the system is at R. Show that L, the
total an
2. Forces
In this section, we describe a number of dierent forces that arise in Newtonian mechanics. Throughout, we will restrict attention to the motion of a single particle. (Well
look at what happens when we have more than one particle in Section 5). W
7. Special Relativity
Although Newtonian mechanics gives an excellent description of Nature, it is not universally valid. When we reach extreme conditions the very small, the very heavy or
the very fast the Newtonian Universe that were used to needs repla
4. Central Forces
In this section we will study the three-dimensional motion of a particle in a central
force potential. Such a system obeys the equation of motion
mx = V (r )
(4.1)
where the potential depends only on r = |x|. Since both gravitational and
6. Non-Inertial Frames
We stated, long ago, that inertial frames provide the setting for Newtonian mechanics.
But what if you, one day, nd yourself in a frame that is not inertial? For example,
suppose that every 24 hours you happen to spin around an axis
3. Interlude: Dimensional Analysis
The essence of dimensional analysis is very simple: if you are asked how hot it is outside,
the answer is never 2 oclock. Youve got to make sure that the units agree. Quantities
which come with units are said to have dim
5. Systems of Particles
So far, weve only considered the motion of a single particle. If our goal is to understand
everything in the Universe, this is a little limiting. In this section, we take a small step
forwards: we will describe the dynamics of N ,
Dynamics and Relativity: Example Sheet 1
Professor David Tong, January 2013
1. In one spatial dimension, two frames of reference S and S have coordinates (x, t)
and (x , t ) respectively. The coordinates are related by t = t and
x = f (x, t)
Viewed from f
Dynamics and Relativity: Example Sheet 2
Professor David Tong, February 2013
1. A particle moves in a xed plane and its position vector at time t is x. Let (r, )
be plane polar coordinates and let and be unit vectors in the direction of increasing
r
r and
Michaelmas Term, 2004 and 2005
Preprint typeset in JHEP style - HYPER VERSION
Classical Dynamics
University of Cambridge Part II Mathematical Tripos
Dr David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
2. The Lagrangian Formalism
When I was in high school, my physics teacher called me down one day after
class and said, You look bored, I want to tell you something interesting.
Then he told me something I have always found fascinating. Every time
the subj
4. The Hamiltonian Formalism
Well now move onto the next level in the formalism of classical mechanics, due initially
to Hamilton around 1830. While we wont use Hamiltons approach to solve any further
complicated problems, we will use it to reveal much mo
Lent Term, 2011 and 2012
Preprint typeset in JHEP style - HYPER VERSION
Statistical Physics
University of Cambridge Part II Mathematical Tripos
Dr David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
Wilb
5. Phase Transitions
A phase transition is an abrupt, discontinuous change in the properties of a system.
Weve already seen one example of a phase transition in our discussion of Bose-Einstein
condensation. In that case, we had to look fairly closely to s
3. Quantum Gases
In this section we will discuss situations where quantum eects are important. Well still
restrict attention to gases meaning a bunch of particles moving around and barely
interacting but one of the rst things well see is how versatile the
2. Classical Gases
Our goal in this section is to use the techniques of statistical mechanics to describe the
dynamics of the simplest system: a gas. This means a bunch of particles, ying around
in a box. Although much of the last section was formulated i
4. Classical Thermodynamics
Thermodynamics is a funny subject. The rst time you go through it, you
dont understand it at all. The second time you go through it, you think
you understand it, except for one or two small points. The third time you
go through
Statistical Physics: Example Sheet 3
David Tong, February 2012
1. A Wigner crystal is a triangular lattice of electrons in a two dimensional plane.
The longitudinal vibration modes of this crystal are bosons with dispersion relation
= k . Show that, at l
Statistical Physics: Example Sheet 1
David Tong, January 2012
1. Establish Stirlings formula. Start with
N! =
0
ex xN dx
eF (x) dx.
0
Let the minimum of F be at x0 . Approximate F (x) by F (x0 ) + F (x0 )(x x0 )2 /2 and,
using one further approximation,
2. Kinetic Theory
The purpose of this section is to lay down the foundations of kinetic theory, starting
from the Hamiltonian description of 1023 particles, and ending with the Navier-Stokes
equation of uid dynamics. Our main tool in this task will be the
Statistical Physics: Example Sheet 2
David Tong, February 2012
1. A particle moving in one dimension has Hamiltonian
p2
+ q 4
2m
Show that the heat capacity for a gas of N such particles is CV = 3NkB /4. Explain
why the heat capacity is the same regardles
Michaelmas Term 2012
Preprint typeset in JHEP style - HYPER VERSION
Kinetic Theory
University of Cambridge Graduate Course
David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
Wilberforce Road,
Cambridge,