Lesson 1 of 13 · 7 min

Rigid bodies and their motion

NCERT §6.1

Ananya, 30 kg, spends an evening at the village mela. At the entrance a wooden crate slides down a plank off a tractor trolley, and right beside it a gas cylinder is rolled down another plank. Both reach the ground, but they do it in very different ways.

The story this chapter follows: Ananya at the village mela

Ananya, 30 kg, spends an evening at the village mela. A crate and a cylinder coming off a trolley, an L-shaped signboard, a bursting firework, the giant wheel, the stall door, a see-saw, the fountain motor, a flywheel and finally her father's swivel chair carry the chapter, with the same numbers throughout.

The lesson in notes

In short

A particle is an idealised point mass with no size. Real bodies are extended, and an extended body is best seen as a system of particles.

An ideal rigid body keeps a perfectly definite shape: the distance between every pair of its particles stays fixed. No real body is truly rigid, but wheels, tops, steel beams, molecules and planets can be treated as rigid when their bending, twisting and vibration are negligible.

In pure translation every particle of the body has the same velocity at each instant, like a block sliding down an incline without turning.

A cylinder rolling down the same incline is translating plus rotating: its particles have different velocities at the same instant, and if it rolls without slipping the point in contact with the incline is momentarily at rest.

Fixed along a line, a body has only rotation open to it. Each of its particles then traces a circle whose plane is at right angles to the axis and whose centre lies on it; particles on the axis stay still. A ceiling fan and a potter's wheel turn this way, and so do the giant wheel and merry-go-round at a fair.

In some rotations only one point is fixed and the axis moves: a spinning top's axis sweeps out a cone about the vertical through its tip (precession), and an oscillating table fan's axis swings about its pivot.

Summary: a body that is not pivoted either translates or translates and rotates; a pivoted or fixed body rotates. This chapter treats rotation about a fixed axis only.