Mathematics can be made to describe the real world, but the description is always imperfect because the amount of data that would have to be collected and the complexity of the model would be too great to be particle. By making assumptions that are accurate to a high degree we can capture all the essential features of the situation while greatly reducing the complexity of the calculations.
Simplifying assumptions that are often made include the following:
Strings are assumed to be inextensible. This means that when the string becomes taut, any particles moving in a straight line connected at either end move at any instant with the same velocity and acceleration.
Strings and springs are assumed to be light – they have no mass. This means that we do not have to apply the equation F=ma to the string or spring separately.
Bodies are often assumed to be particles and the equation of motion derived from applications of the equationapplies to the motion of the centre of mass. All forces then act through the centre of mass. This assumption requires that the body not be rotating.
Beams are assumed to be rigid. They do not bend and have no thickness. This means that no matter what forces are applied, lengths remain the same.
Friction is assumed to be a constant force or to be a constant fraction of the normal reaction force. In fact friction is not constant. Once a body starts to move the friction force tends to decrease and even while a body is moving the friction force is not constant.
Air resistance is often ignored. This means that for a body moving through the air subject to the force of gravity, the acceleration is 9.8 m/s2 downwards and the horizontal velocity is constant.
Collisions are often assumed to be instantaneous and bodies involved in collisions are assumed to be point particles.
One body involved in a collision – often a wall or a floor – is assumed to be fixed and experiences no change in velocity- which remains zero – as a result of the collision.
Pulleys are assumed to be smooth, having no friction. This means that the tension in any string passing over the pulley is the same throughout the length of the string.
Contact durfaces are often assumed to be smooth so there is no friction.