Mechanics Edexcel A-level Maths

Particle

Dimensions of the objects are negligible (Ignore rotational forces and air resistance)

Rod

All dimensions but one are negligible, like a pole or a beam and is rigid

Lamina

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

Uniform body

Mass is distributed evenly

Light object

Mass of the object is small compared to other masses, like a string or a pulley (light string - tension is the same throughout)

Inextensible string

A string that does not stretch under load (acceleration of connected particles is the same)

Rough surface

If a surface is not smooth, it is rough

Wire

Rigid thin length of metal

Smooth and light pulley

All pulleys you consider will be smooth and light

Bead

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

Peg

A support from which a body can be suspended or rested

Air resistance

Resistance experienced as an object moves through the air

Gravity

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

What is assumed when modelling a particle?

Mass of the object is concentrated at a single point

Rotational forces and air resistance can be ignored

What is assumed when modelling a rod?

Mass is concentrated along a line

No thickness

Rigid (does not bend or buckle)

What is assumed when modelling a lamina?

Mass is distributed across a flat surface

What is assumed when modelling a uniform body?

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

What is assumed when modelling a light object?

Treat object as having zero mass

Tension the same at both ends of a light string

What is assumed when modelling inextensible string?

Acceleration is the same in objects connected by a taught inextensible string?

What is assumed when modelling a smooth surface?

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

What is assumed when modelling a rough surface?

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

What is assumed when modelling a wire?

Treated as one-dimensional

What is assumed when modelling a smooth and light pulley?

Pulley has no mass

Tension is the same on either side of the pulley

What is assumed when modelling a bead?

Moves freely along a wire or string

Tension is the same on either side of the bead

What is assumed when modelling a peg?

Dimensionless and fixed

Can be rough or smooth as specified in question

What is assumed when modelling a air resistance?

Usually modelled as being negligible

What is assumed when modelling a gravity?

Assume that all objects with mass are attracted towards the Earth

Earth's gravity is uniform and acts vertically downwards

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

SI unit for mass

kilogram (kg)

SI unit for length/displacement

metre (m)

SI unit for time

second (s)

SI unit for speed/velocity

meters per second (m/s)

SI unit for acceleration

meters per second per second (m/s^2)

SI unit for weight/force

newton (N (= kg m/s^2))

Weight

Force that acts vertically downward on an object

Normal reaction

Force which acts perpendicular to a surface when an object is in contact with the surface

Friction

Force which opposes the motion between two rough surfaces

Tension in the string

Force acting on an object if being pulled along by a string

Thrust or compression in rod

The force acting on an object being pushed along using a light rod

Buoyancy

Upward force on a body that allows it to float or rise when submerged in a liquid

Vector quantity

A quantity that has both magnitude and direction

Displacement

Distance in in a particular direction

Velocity

Rate of change of displacement

Acceleration

Rate of change of velocity

Force/weight

Described by magnitude, direction and point of application

Scalar quantity

A quantity that only has magnitude

Distance

Measure of length

Speed

Measure of how quickly a body moves

Time

Measure of ongoing events taking place

Mass

Measure of the quantity of matter contained in an object

i

x direction

j

y direction

SUVAT equations

s = ut + 1/2at^2

s = vt - 1/2at^2

s = (u+v)/2*t

v = u + at

v^2 = u^2 + 2as

What is the downward acceleration of an object moving vertically downward due to gravity?

9.8ms^-2

Newton's first law of motion

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Newton's Second Law of Motion

The force needed to accelerate a particle is equal to the prodcut of the mass of the particle and the acceleration produced

Smooth pulley

The tension is the same on both sides of the pulley

Newton's third law

For every action there is an equal and opposite reaction

Rigid body

a body that maintains a constant shape

Moment

F x dsinθ

Inclined plane

Limiting value of friction

μR

Horizontal motion of a projectile

constant velocity

Vertical motion of a projectile

constant acceleration due to gravity

Projection motion formula

Force on a pulley

2Tcos(θ/2)