# Inertia

### Keywords

mass, inertia, electron, proton, neutron
Inertia is a property of matter by which it resists our attempts to accelerate it. We are accustomed to call this property mass. Mass is very fundamental in classical physics, but the only fundermental way of measuring it is by comparing objects with a standard mass, a process which usually relies on the fact that the force of gravity acting on an object is proportional to its mass. Newton identified two types of mass; inertial mass and gravitational mass and asserted that they were the same thing. The word mass also has a third meaning in common usage which is "the amount of matter" in an object. The every day use of the word weight also refers to "the amount of matter" in an object.

One of the great aims of science teachers everywhere is to get pupils to understand the difference between mass meaning the amount of matter in an object and weight meaning the force with which the earth is pulling an object downwards. Generally speaking this is quite unsuccessful and most science teachers hardly ever use the words correctly in the staff room!

The point I want to make is that even scientists have an internalized concept of mass which relates more to the common usage of the words mass and weight than to anything else. In the appropriate situation, they can recite the correct formula of words and everything seems well, but when it comes to electrons, protons and neutrons, this imprecise internalized concept translates into something which is "real" in a magical sort of a sense. The old billiards ball concept of gas atoms is reborn in the electrons, neutrons and protons of the atoms.

Let us forget all about the words mass and weight for a while and think only of Inertia. This is a property we can observe in all objects which are free to be moved. When we exert a force, they start to move slowly gaining speed. Sometimes the effect can be quite dramatic as when an arrow is shot from a bow, and at other times it can be almost imperceptible as when a man on the quay pushes against a super-tanker. The arrow and the super-tanker possess inertia as do the electrons within the television tube. They escape from the red hot surface of the electron gun filament and are accelerated by 15,000 volts or more.

The acceleration is proportional the force but inversely proportional to the inertia. The super-tanker has a very great inertia, while the arrow has a small inertia and the electron a very very very small inertia. Newtons second law applies, but we must read the m as "inertial mass". We can model an electron with a pure charge. We do not need any mass, just the surface of the charge and its surrounding electric field. Such a charge has inertia. It resists the accelerating force of the intense electric field within the television tube and its speed remains finite. We do not need a magical ingredient called mass. It is the energy stored in the electric field of the charge which gives it its inertia. The inertia of a pure charge depends on the amount of energy stored in the electric field and this is fixed by the quantity of charge and by the radius of the surface of the charge.

The inertial mass of a pure charge is: See the mathematical proof of this