Applied Maths Mechanics Introduction

Particle - dimnesions of the object are negligible (so small or unimportant as to be not worth considering; insignificant)

mass of the object is concentrated at a single point

rotational forces and air resistance can be ignored

rod - all dimensions but one are negligbile - like a pole or a rod

mass is concentrated along a line

no thickness

rigid - does not bend or buckle

lamina - objects with area but negligbile thickness like a sheet of paper

mass is distributed across a falt surface

uniform body - mass is distributed evenly

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

treat object as having zero mass

tension the same as both ends of a light strign

inextensible string - a string tha does not stretch under load

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

smooth surface

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

rough surface

objects in contact with the surface experience a frictional force if there are movign or are acted on by a force

wire - rigid thin length of metal

treat as 1 dimensional

smooth and light pulley- all pulleys you consider will be smooth and lighjt

pulley has no mass

tension is the same on either side of the pulley

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

moves fgreely along a wire or string

tension is the same on either side of the bead

peg - a support from whihc a body can be suspended or rested

dimensionless and fixed

can be rough or smooth as specified in questiona

air resistance - resistance experienced as an object moves through thte air

usually modelled as being negligible

gravity - force of attraction between all objects. Acceleration due to gravity is denoted by g

assume that all objects with mass are attracted topwards the earth

earth gravity is uniform and acts verticall downwards

g is constants and is taken as 9.8ms^-1 unless stated