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CLASSICAL MECHANICS
Chapter 1. Centres of Mass
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
Introduction and Some Definitions
Plane Triangular Lamina
Plane Areas
Plane Curves
Summary of the Formulas for Plane Laminas and Curves
The Theorems of Pappus
Unifor
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APPENDIX B
Solutions to Miscellaneous Problems
1.
b = 10 m
a= 8m
l
k
h =3 m
m
n
x
By proportions,
hn
hm
hh
= 1.
=
and
=
and therefore +
kx
l
x
k
l
Therefore by Pythagoras:
1
h
+
a2 x2
= 1.
2
2
b x
1
Everything but x is known in this equation, which c
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APPENDIX A
Miscellaneous Problems
In this Appendix I offer a number of random problems in classical mechanics. They are
not in any particular order they come just as I happen to think of them, and they are not
necessarily related to any of the topics di
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CHAPTER 20
MISCELLANEA
20.1 Introduction
This chapter is a miscellany of diverse and unrelated topics namely surface tension, shear
modulus and viscosity discussed only for the purpose of presenting a few more examples of
elementary problems in mechanic
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CHAPTER 19
THE CYCLOID
19.1
Introduction
FIGURE IXX.1
2
P
y
1.5
1
2
0.5
0
0
P
0.5
1
1.5
x
2
A
2.5
3
Let us set up a coordinate system Oxy, and a horizontal straight line y = 2a. We imagine a circle of
diameter 2a between the x-axis and the line y = 2a,
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CHAPTER 18
THE CATENARY
18.1
Introduction
If a flexible chain or rope is loosely hung between two fixed points, it hangs in a curve that looks a
little like a parabola, but in fact is not quite a parabola; it is a curve called a catenary, which is a
wor
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CHAPTER 17
VIBRATING SYSTEMS
17.1 Introduction
A mass m is attached to an elastic spring of force constant k, the other end of which is
attached to a fixed point. The spring is supposed to obey Hookes law, namely that,
when it is extended (or compressed
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CHAPTER 16
HYDROSTATICS
16.1 Introduction
This relatively short chapter deals with the pressure under the surface of an
incompressible fluid, which in practice means a liquid, which, compared with a gas, is
nearly, if not quite, incompressible. It also
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CHAPTER 15
SPECIAL RELATIVITY
15.1. Introduction
Why a chapter on relativity in a book on classical mechanics? A first excuse might be
that the phrase classical mechanics is used by different authors to mean different
things. To some, it means pre-relat
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CHAPTER 14
HAMILTONIAN MECHANICS
14.1 Introduction
The hamiltonian equations of motion are of deep theoretical interest. Having established
that, I am bound to say that I have not been able to think of a problem in classical
mechanics that I can solve m
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CHAPTER 13
LAGRANGIAN MECHANICS
13.1 Introduction
The usual way of using newtonian mechanics to solve a problem in dynamics is first of
all to draw a large, clear diagram of the system, using a ruler and a compass. Then mark
in the forces on the various
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CHAPTER 12
FORCED OSCILLATIONS
12.1 More on Differential Equations
In Section 11.4 we argued that the most general solution of the differential equation
ay" + by ' + cy = 0
11.4.1
y = Af ( x ) + Bg ( x ).
11.4.2
is of the form
In this chapter we shall b
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CHAPTER 11
SIMPLE AND DAMPED OSCILLATORY MOTION
11.1
Simple Harmonic Motion
I am assuming that this is by no means the first occasion on which the reader has met simple
harmonic motion, and hence in this section I merely summarize the familiar formulas
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CHAPTER 10
ROCKET MOTION
1. Introduction
If you are asked to state Newton's Second Law of Motion, I hope you will not reply: "Force
equals mass times acceleration" because that is not Newton's Second Law of Motion.
Newton's Second Law of Motion is:
The
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CHAPTER 9
CONSERVATIVE FORCES
9.1 Introduction.
In Chapter 7 we dealt with forces on a particle that depend on the speed of the particle. In
Chapter 8 we dealt with forces that depend on the time. In this chapter, we deal with forces that
depend only on
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CHAPTER 8
IMPULSIVE FORCES
8.1 Introduction.
As it goes about its business, a particle may experience many different sorts of forces. In
Chapter 7, we looked at the effect of forces that depend only on the speed of the particle. In a
later chapter we sh
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CHAPTER 7
PROJECTILES
7.1 No Air Resistance
We suppose that a particle is projected from a point O at the origin of a coordinate system,
the y-axis being vertical and the x-axis directed along the ground. The particle is projected in
the xy-plane, with
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CHAPTER 6
MOTION IN A RESISTING MEDIUM
6.1 Introduction
In studying the motion of a body in a resisting medium, we assume that the resistive force on a
body, and hence its deceleration, is some function of its speed. Such resistive forces are not
genera
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CHAPTER 5
COLLISIONS
5.1 Introduction
In this chapter on collisions, we shall have occasion to distinguish between elastic and inelastic
collisions. An elastic collision is one in which there is no loss of translational kinetic energy. That
is, not only
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CHAPTER 4
RIGID BODY ROTATION
4.1 Introduction
No real solid body is perfectly rigid. A rotating nonrigid body will be distorted by
centrifugal force* or by interactions with other bodies. Nevertheless most people will
allow that in practice some solids
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CHAPTER 3
SYSTEMS OF PARTICLES
3.1 Introduction
By systems of particles I mean such things as a swarm of bees, a star cluster, a cloud of
gas, an atom, a brick. A brick is indeed composed of a system of particles atoms
which are constrained so that the
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CHAPTER 2
MOMENT OF INERTIA
2.1 Definition of Moment of Inertia
Consider a straight line (the "axis") and a set of point masses m1 , m2 , m3 , K such that the
distance of the mass mi from the axis is ri . The quantity mi ri 2 is the second moment of the
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CHAPTER 1
CENTRES OF MASS
1.1 Introduction, and some definitions.
This chapter deals with the calculation of the positions of the centres of mass of various bodies.
We start with a brief explanation of the meaning of centre of mass, centre of gravity an