# Newton's laws of motion

**First and second laws**

If you are considering the forces acting on just one body, either law I or law II will apply.

**The first law** describes what happens when the forces acting on a body are balanced (no resultant force acts) – the body remains at rest or continues to move at constant velocity (constant speed in a straight line).

If a book is placed on a table, it stays at rest. This is an example of Newton’s first law. There are two forces on the book and they happen to balance owing to the elastic properties of the table. The table is slightly squashed by the book and it exerts an elastic force upwards equal to the weight of the book. You can show this by placing a thick piece of foam rubber on a table and placing a book on top of it. The foam rubber squashes.

Galileo was the first person to challenge the commonsense notion that steady motion requires a steady force. He looked beyond the obvious and was able to say *if* there was no friction *then* an object would continue to move at constant velocity. In other words, he put forward a hypothesis. He could see that a motive force is generally needed to keep an object moving in order to balance frictional forces opposing the motion.

The motion of air molecules is a good example to consider with students. When air temperature is constant, no force is applied to keep air molecules moving, yet they do not slow down. If they did, in a matter of minutes the air would condense into a liquid.

**The second law** describes what happens when the forces acting on a body are unbalanced (a resultant force acts). The body changes its velocity, *v*, in the direction of the force, *F*, at a rate proportional to the force and inversely proportional to its mass, *m*. The rate of change of *v* is proportional to *F* /*m*. And rate of change of velocity is acceleration, *a*.

So if the table mentioned above were in an upwardly accelerated lift, an outside observer would see that the two forces acting on the book were unequal. The resultant force would be sufficient to give the book the same upward acceleration as the lift. Put some bathroom scales between the book and the table. If the book is accelerating downwards, its weight would be greater than the reaction force from the table. The book would, however, appear to be weightless.

Mass is measured in kilograms and acceleration in *m* /s^{2}. With an appropriate choice of unit for force, then the constant of proportionality, k, in the equation *F = *k*ma* is 1. This is how the newton is defined, giving *F* = *ma* or *a* = *F* /*m*.

This can also be expressed as *F* = rate of change of momentum or *F* = Δ*p* / Δ*t*.

Newton wanted to understand what moves the planets. He realized that a planet requires no force along its orbit to move at constant speed, but it does require a force at right angles to its motion (gravitational attraction to the Sun) to constantly change direction.

**The third law**

Newton’s third law can be stated as ‘interactions involve pairs of forces’. Be careful in talking about third law pairs (often misleadingly called ‘action’ and ‘reaction’). Many students find this law the most difficult one to understand.

Returning to the book on a table, there are three bodies involved: the Earth, the book, and the table. In this example, the interaction pairs of forces are:

- the weight of the book and the pull of the book on the Earth (gravitational forces)
- the push of the book on the table and the push of the table on the book (contact forces)

In general, action and reaction pairs can be characterized as follows:

- they act on two different bodies
- they are equal in magnitude but opposite in direction
- they are the same type of force (e.g. gravitational, magnetic, or contact)