Negligible - Examples - in Physics

In Physics

Any macroscopic system is always much more complicated than any idealized mathematical model describing it. In order to simplify real situations, some effects are generally regarded as insignificant because their magnitude is so small as to be negligible. Given a system described by a formula it is sometimes possible to make a Taylor expansion of the expression and then identify negligible terms.

An example would be a car moving at 10 km/h along a straight horizontal road. In total, there are five main forces acting on this car, gravity on the mass of the car (the weight), the reaction force of the road opposing the weight, the friction of the wheels on the road, the force of the engine, and air resistance against the car. The forces that have the most effect on the car will be the weight, the reaction opposing the weight and the friction. In order to describe the motion of the car mathematically, to a reasonable precision, only four of the forces has to be included, weight, engine, reaction and friction. Air resistance is "negligible" and can be disregarded because the car is moving at such a low speed. Even though air resistance has an effect, the effect is so minuscule that for most purposes it is safe to regard it as not being there at all, so to avoid any unnecessarily complicated calculations. At greater speeds, air resistance becomes significant and can no longer be neglected.