Ch 7System of Particles and Rotational Motion — concept-first.

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.

Before we can analyse the motion of a rigid body, we must first understand what kinds of motion are even possible for it.

When we study the motion of a system of particles — whether it's two atoms or a spinning cricket bat — we quickly realise that tracking every single particle is impractical.

When we studied the centre of mass of a system of particles, we defined it as a weighted average position.

The idea of linear momentum extends naturally from a single particle to a collection of particles. For a system, the total linear momentum is simply the vector sum of the momenta of all the individual…

When two vectors are multiplied in a way that the result is a vector, the operation is called a vector product or cross product.

When a rigid body rotates about a fixed axis, different points on the body move with different linear speeds.

When a rigid body rotates, its angular velocity can change with time — just as a car’s linear velocity changes when it accelerates.

The connection between force and linear motion is straightforward — force causes linear acceleration. For rotational motion, the analogous quantity is torque, which causes angular acceleration.

When you push a door, where you push matters just as much as how hard you push. Push near the hinges — the door opens slowly, with effort. Push at the far edge — it swings open easily.

The idea of angular momentum is the rotational analogue of linear momentum. Just as linear momentum () tells us how much "oomph" a moving object has in a straight line, angular momentum tells us how m…

When we shift from studying general systems of particles to rigid bodies, the effect of external forces becomes richer.

A rigid body is said to be in translational equilibrium when its centre of mass moves with constant velocity (or is at rest). That requires the net external force on the body to be zero:

Every particle on Earth experiences a gravitational pull toward the planet's centre. For a body made of many particles, each particle has its own weight acting vertically downward.

When you push a stationary object, it starts moving in a straight line. The resistance it offers to that change in its state of motion is called mass — a measure of its inertia in linear motion.

You already know how to describe motion along a straight line using displacement, velocity, and acceleration — all linked by the equations of motion.

The previous sections built the language of rotational motion — angular displacement, velocity, acceleration, moment of inertia, and torque. Now we put these tools to work.

When a rigid body rotates about a fixed axis, every particle of the body moves in a circle centred on that axis. Each particle therefore carries angular momentum about the axis.

The conservation of angular momentum is the rotational twin of the conservation of linear momentum. Just as the linear momentum of an isolated system remains constant when no external force acts, the…

- Centre of mass of a system is the weighted average position: . For a rigid body, it behaves as if the entire mass is concentrated there for translational motion.

1. To figure out how the centre of mass of a system moves, you don't need to know anything about the internal forces between the particles. Only the external forces acting on the system matter.

The end-of-chapter exercises from the NCERT textbook.

Higher-order thinking problems from the NCERT Exemplar.