# Table of Contents

- Page ID
- 19041

Classical mechanics is the study of the motion of bodies (including the special case in which bodies remain at rest) in accordance with the general principles first enunciated by Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia.

## 2: Moments of Inertia

In this chapter we shall consider how to calculate the (second) moment of inertia for different sizes and shapes of body, as well as certain associated theorems. But the question should be asked: "What is the purpose of calculating the squares of the distances of lots of particles from an axis, multiplying these squares by the mass of each, and adding them all together?## 5: Collisions

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 must no translational kinetic energy be degraded into heat, but none of it may be converted to vibrational or rotational kinetic energy. In laying out the principles involved in collisions between particles, we need not suppose that the particles actually "bang into" each other.## 6: Motion in a Resisting Medium

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 generally conservative, and kinetic energy is usually dissipated as heat.## 9: Conservative Forces

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path.## 13: Lagrangian Mechanics

Sometimes it is not all that easy to find the equations of motion and there is an alternative approach known as lagrangian mechanics which enables us to find the equations of motion when the newtonian method is proving difficult.## 14: Hamiltonian Mechanics

Hamiltonian mechanics can be used to describe simple systems such as a bouncing ball, a pendulum or an oscillating spring in which energy changes from kinetic to potential and back again over time, its strength is shown in more complex dynamic systems, such as planetary orbits in celestial mechanics. The more degrees of freedom the system has, the more complicated its time evolution.## 15: Special Relativity

The phrase “special” relativity deals with the transformations between reference frames that are moving with respect to each other at constant relative velocities. Reference frames that are accelerating or rotating or moving in any manner other than at constant speed in a straight line are included as part of general relativity and are not considered in this chapter.## 16: Hydrostatics

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 deals with Archimedes’ principle and the equilibrium of floating bodies. The chapter is perhaps a little less demanding than some of the other chapters, though it will assume a familiarity with the concepts of centroids and radius of gyration.## 18: The Catenary

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 word derived from the Latin catena, a chain.## 20: Miscellaneous

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 mechanics. It is not intended in any way to substitute for a comprehensive course in any of the vast and interesting fields of surface chemistry, elasticity or hydrodynamics.