# Rigid Bodies

## Understanding Rigid Bodies

• A rigid body is an idealisation of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it.
• The motion of a rigid body can be described in several ways, including its translation (linear motion along a path) and rotation (spinning about an axis).
• Both its translation and rotation characteristics are defined with respect to its centre of mass.

## Centre of Mass in Rigid Bodies

• The centre of mass of a rigid body under gravity acts as a single point where all its weight is concentrated.
• Each rigid body has one unique centre of mass, regardless of its shape and uniformly distributed mass.

## Calculation of Centre of Mass in Rigid Bodies

• If the body is uniform and symmetrical, the centre of mass will be at the geometrical centre.
• For flat, irregular shaped objects, the centre of mass can be located by suspending the object from various points and drawing a vertical line downwards - the point of intersection of these lines will be the centre of mass.
• If the body consists of a combination of regular shapes, the centre of mass can be found separately for each shape and then combined considering the masses and distances of individual centres of mass from a common reference (usually any one end or the centre).

## Motion of Rigid Bodies

• If a force is applied through the centre of mass of a rigid body, it will translate, but not rotate.
• If a force is applied elsewhere, it will cause both translation and rotation.

## Principle of Moments for Rigid Bodies

• The principle of moments is crucial to understanding the equilibrium of a rigid body.
• When a rigid body is in equilibrium, the sum of the moments about any point is zero. This is an application of the principle of moments, and is essential to understanding the behaviour of beams, seesaws, levers and other structures within the context of rigid bodies.

## Practical Applications of Rigid Body Dynamics

• Rigid body dynamics, including the concept of the centre of mass and its associated principles, are key in fields like engineering, architecture and physics.
• Understanding these enables the design of stable structures, the prediction of the behaviour of machinery parts, and the analysis of motion in physical systems.