- A-Level Maths

# Modelling in Mechanics

The real world of mechanics is incredibly complicated, with hundreds of different factors affecting motion and stability. This would be near impossible to calculate at this stage, so to simplify it we model objects and scenarios in a number of different ways.

## Modelling Assumptions

### Particle

Has negligible dimensions

Mass acts about a single point

Rotational forces and air resistance can be ignored

### Rod

The diameter is negligible (so no thickness), only length counts

Mass acts along a line

It is rigid, so does not bend or buckle

### Lamina

An object with only area, thickness is negligible (like a sheet of paper)

Mass acts across the flat surface

### Uniform Body

The Mass is distributed evenly throughout the object

The mass is modelled to act through one point, the

**centre of mass**, in the geometrical middle of the body

### Light Object

The mass of the object is negligible

Often used for strings or pulleys

Allows us to model the tension on each end of a string as equal

### Inextensible String

A string that does not stretch when a force is applied

Allows us to model the acceleration of two connected particles as the same

### Smooth Surface

There is no friction between the surface and any object on it

### Rough Surface

There is friction between the surface and any object on it

### Wire

A rigid length of metal with negligible thickness (only modelled with length)

### Smooth and Light Pulley

The pulley has no mass

No friction in the pulley, so tension is the same either side of it

### Bead

A particle with a hole in it for string/wire to be threaded through