Mechanics deals with the action of forces acting upon objects. In real-world problems many factors must be accounted for that could add complications - in order to simplify a problem we can create a mathematical model with certain modelling assumptions to allow us to carry out an analysis.
These modelling assumptions are: to ignore air resistance; to have a perfect bounce on a flat pitch; to have a constant force due to gravity and to model a ball as a particle.
An object can be modelled as a particle if it is small in comparison to other sizes or lengths. Modelling an object as a particle means it has no dimensions and that the mass of the object is concentrated at a single point - therefore we can ignore effects due to air resistance and rotational effects of forces acting upon it.
An object, such as a ruler or a beam, can be modelled as a rod if it has one dimension small in comparison with the other. Modelling an object as a rod means the mass can be considered to be distributed along a straight line. The rod has no thickness (is one dimensional) and does not bend or buckle (is rigid).
An object, such as a piece of metal, whose thickness is very small compared to its length and width can be modelled as a lamina. Modelling an object as a lamina means that its mass can be considered to be distributed across a flat surface as it has no thickness.
An object can be said to have its mass evenly distributed over its entire volume if it is uniform.This means it has a centre of mass - the point where the mass of the body is concentrated. This is not necessarily the mid-point of the object.
We can model an object, such as strings or pulleys, as being light if its mass is very small compared to other objects. If an object is light we can ignore its mass.
Strings will usually be modelled as inextensible, meaning they do not stretch under a load.
A smooth surface ignores the effects of friction.
If a surface considers frictional effects it is said to be rough.
A wire can be smooth or rough and is considered as a rigid thin length of metal, which is treated as being one-dimensional.
Pulleys are modelled as being smooth (no friction) and light (having zero mass).
A bead is a particle that can be threaded onto a wire or string and move freely along it.
A peg is treated as a single point with no dimensions, from which an object can be suspended or rest upon. A peg can be rough or smooth.
The resistance experienced when an object moves through air due to friction. Air resistance can be modelled as negligible.
Unless specified wind is ignored.
Gravity is the force of attraction between all objects with a mass. The force of the Earth's gravity is modelled as being uniform and acts vertically downwards. The acceleration due to gravity is denoted $g$ and is assumed constant at $9.8 \mathrm{ms}^{-2}$.