1
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
1
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
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 t
1
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
1
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
1
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 pa
1
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 Hook
1
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
1
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 author
1
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
1
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 rule
1
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
1
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
1
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 Secon
1
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. I
1
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
1
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 g
1
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 func
1
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
1
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. Neverthel
1
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 syste
1
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 i
1
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