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 is ri . The quantity mi ri 2 is the second moment of the

1 CHAPTER IXX THE CYCLOID 19.1 Introduction
FIGURE IXX.1 2
P
1.5
1
2
y
0.5
0
0 0.5 1 1.5 x 2
P
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,

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 parabola; it is a curve called a catenary, which is a wor

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 Hookes law, namely that, when it is extended (or compressed

CHAPTER 16 HYDROSTATICS 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 deal

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 authors to mean different things. To some, it means pre-relat

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 of a problem in classical mechanics that I can solve m

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 ruler and a compass. Then mark in the forces on the various

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
is of the form
y = Af ( x ) + Bg ( x ).
11.4.2
In this chapter we shall b

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 this section I merely summarize the familiar formulas

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 Second Law of Motion. Newton's Second Law of Motion is: The

CHAPTER 9 CONSERVATIVE FORCES 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 th

1 CHAPTER 8 IMPULSIVE FORCES 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 sha

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 ground. The particle is projected in the x y-plane, wit

1 CHAPTER 6 MOTION IN A RESISTING MEDIUM 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 general

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 m

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. Nevertheless most people will allow that in practice some solids

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 system of particles atoms which are constrained so that ther

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 a few more examples of elementary problems in mechanic