Simplifying Assumptions
The world is a very complicated place, where everything may be analysed down to the
degree and the meaning of every detail endlessly considered. In physics however, we always seek the simplest working model, and detail which is not needed is discarded. When considered the forces acting on objects and the motion of objects we make the assumptions listed below.
A string connecting any two bodies is inextensible. This means it stores no energy, and if it is taut, the velocity and acceleration of any connected bodies is the same. It also means, very importantly that when the string is taut, the tension is always the same throughout the string, and always acts towards the centre.
A ladder or rod is inextensible, incompressible and inflexible. This means it does not stretch, shrink or bend and does not store energy.
Bodies are often considered as particles, so they may be thought to have no size. They are taken to be a point mass acting at their centre of mass. This means we can apply
to the body with
and
being the force applied to the centre of mass and the acceleration of the centre of mass respectively.
Surfaces are considered to be smooth. No surface is ever smooth but if friction is negligible we may ignore it.
Pulleys are considered to be smooth. There are in fact always frictional forces in the bearings, but the torque of these is usually small and can be ignored.
Air resistance or friction are often ignored, since they are often negligible.
The radius of the Earth is ignored when finding changes in gravitational potential. This means we use
and not
Forces are assumed to act instantaneously and stop instantaneously, as when a string tightens or becomes taut.
Forces may be assumed to be constant, for example when a hammer strikes a post in the ground, the hammer is assumed to experience a constant force of resistance before it comes to rest.
A lamina does not bend. It is usually assumed to have uniform density so that it's centre of gravity is always in the middle.