Introduction

Mechanics is the branch of physics concerned with motion. It splits naturally into two large domains: statics, the study of objects at rest or in equilibrium under balanced forces, and kinetics, the study of objects that are actually moving. Kinetics itself has two complementary halves. Kinematics describes motion -- distance, displacement, speed, velocity, acceleration -- without asking what causes it. Dynamics goes one step further and describes motion along with its cause, which is force (for translational/linear motion) and torque (for rotational motion); the quantities of interest here are momentum, force, energy and power in addition to the kinematic ones.

A crucial idea that this chapter leans on repeatedly is that motion is a relative concept. Whether an object is 'moving' or 'at rest' can only be answered with respect to a chosen frame of reference. A passenger sitting quietly inside a moving bus is at rest relative to the bus but in motion relative to the ground; both descriptions are equally valid, they simply refer to different frames.

Real motion, however complicated, can often be resolved into simpler categories depending on the relationship between the initial velocity $\vec{u}$ and the acceleration $\vec{a}$: if $\vec{u}=0$, any acceleration produces linear motion; if $\vec{u}\neq 0$ and $\vec{a}$ is along the same or opposite line as $\vec{u}$, the motion stays linear; if $\vec{a}$ is always perpendicular to the velocity, the path is circular; if $\vec{a}$ is constant but not aligned with $\vec{u}$, the path is a parabola (e.g. projectile motion); any other relationship between $\vec{u}$ and $\vec{a}$ gives more complex trajectories. This chapter itself is built around dynamics: Newton's three laws of motion, the different kinds of forces bodies experience, work, energy and power, momentum and its conservation in collisions, and finally the rotational analogues of force (torque) and the useful idea of a body's centre of mass.