# How do we state Newton's Laws?

Jun 3, 2016

Newton has a number of laws, including a law of cooling, but when we say 'Newton's Laws' we usually mean his laws of motion. These are listed and discussed below.

#### Explanation:

There are a number of ways of stating Newton's Laws of Motion. The following is the way I have arrived at after years of teaching them. These are the clearest and easiest for students to understand and the least likely to lead to misconceptions (at least in my opinion).

Newton's First Law:

An object remains at rest, or in motion at constant velocity, unless acted upon by an unbalanced external force.

'Constant velocity' means the same speed and the same direction, and is often expressed as 'uniform motion in a straight line'.

An unbalanced force means there has to be a resultant force acting.

Newton's First Law describes inertia: a property of mass that means it requires a force to change its velocity. That includes changing either its direction or its speed or both.

Because motion is relative, we cannot tell whether something is at rest or in constant velocity motion. It depends on the reference frame.

Newton's Second Law:

$\text{acceleration"="force"/"mass}$

$a = \frac{F}{m}$

The acceleration of an object, when a force acts on it, is directly proportional to the force (the greater the force the greater the acceleration) and inversely proportional to the mass (the greater the mass the less the acceleration).

Sometimes also expressed as $F = m a$, which is the same thing.

Newton's Third Law:

For every force there is another force of the same magnitude, acting in the opposite direction. These forces act on different objects.

This is often stated as 'for every action there is an equal and opposite reaction', but which force is the action and reaction depends on our choice, and the notion of 'action forces' tends to cause misconceptions on the part of students.

The Third Law simply means that, for example, if the earth exerts a force on a person, the person exerts a force of the same magnitude (size) on the earth. The Second Law means that the person will accelerate much, much more than the earth (we will not notice the earth's acceleration). Rockets use the Third Law to accelerate forward by accelerating fuel backward. If someone dives off a rowboat in one direction, the boat will move off in the opposite direction.

The three laws of motion work together, and we could even argue that if we understand the Second Law properly, the First Law is not needed, because it is just the case when $F = 0$. Understanding these laws means we understand force, mass and acceleration and their operation much better.