Maths Mechanics models and assumptions

particle

dimensions of the object are negligbile

particle assumptions

• mass of the object is concentrated at a single point

• rotational forces and air resistance can be ignored

rod

all dimensions but one are negligible, like a pole or a beam

rod assumptions

• mass is concentrated along a line

• rigid (does not bend or buckle)

Lamina

object with area but negligible thickness, like a sheet of paper

Lamina assumptions

• mass is distributed across a flat surface

Uniform body

mass is distributed evenly

uniform body assumptions

• mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass

Light object

mass of the object is small compared to other masses, like a string or a pulley

Light object assumptions

• treat object as having zero mass

• tension the same at both ends of a light string

Inextensible string

String that does not stretch under load

Inextensible string assumptions

• acceleration is the same in objects connected by a taut inextensible string

Smooth surface assumptions

• assumes that there is no friction between the surface and any object on it

Rough surface

if a surface is not smooth, then it is rough

Rough surface assumptions

• objects in contact with the surface experience a frictional force if they are moving on are acted on by a force

Wire

Rigid thin length of metal

Wire assumptions

• treated as one dimensional

Smooth and light pulley assumptions

• pulley has no mass

• tension if the same on either side of the pulley

Bead

particle with a hole in it for threading on a wire or string

Bead assumptions

• moves freely on a wire or a string

• tension is the same on either side of the bead

Peg

A support from which a body can be suspended or rested

Peg assumptions

• dimensionless and fixed

• can be rough or smooth as specified in question

Air resistance

resistance experienced as an object moves through the air

Air resistance assumptions

• usually modelled as being negligible

Gravity

Force of attraction between all objects on

• Acceleration due to gravity denoted by ‘g’

Gravity assumptions

• assumes that all objects with mass are attracted towards the earth

• Earth’s gravity is uniform and acts vertically downwards

• g is constant and taken as 9.8ms^-2, unless otherwise stated in the question