Physics · Ch 7 — System of Particles and Rotational Motion
Introduction
Introduction
Why the Particle Model Falls Short
In earlier chapters, we treated every object as a single particle — a point with mass but no size. That worked well for a ball thrown across a room or a stone dropped from a tower. But real objects have finite size. A spinning top, a rolling wheel, or a bending beam cannot be described by the motion of just one point. The particle model is inadequate for extended bodies.
An extended body is, at its core, a system of particles — millions or billions of them, each obeying Newton's laws. To understand how such a body moves as a whole, we need a new idea: the centre of mass. This single point captures the average position of all the mass in the system. Its motion turns out to be surprisingly simple, even when the body itself rotates or deforms.
The Concept of a Rigid Body
Many real-world problems involve bodies that do not change shape appreciably under ordinary forces. A steel beam in a building, a bicycle wheel, a spinning top — these can be treated as rigid bodies.
A rigid body is defined as a body with a perfectly definite and unchanging shape. The distance between any two particles of a rigid body remains constant at all times.
No real body is perfectly rigid — all materials deform to some extent. But in countless situations (wheels, tops, steel beams, molecules, planets), the deformations are so small that we can ignore them. This idealisation makes the mathematics tractable and the results accurate enough for practical use.
What This Chapter Will Do
We begin by studying the motion of a system of particles as a whole, using the centre of mass as our guide. Then we restrict ourselves to rigid bodies, where the internal distances are fixed. This allows us to describe rotation in a clean, powerful way — using angular velocity, torque, and moment of inertia — without worrying about the body warping or vibrating.
The chapter builds a complete framework for rotational motion, parallel to the linear-motion framework you already know. By the end, you will be able to analyse a rolling wheel, a spinning top, or a rotating planet with the same confidence you now bring to a falling stone.
The key shift is from a single particle to a system of particles. The centre of mass is the bridge between the two — it lets us treat the whole system's translational motion as if all mass were concentrated at one point.