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Newton’s first law of motion, inertia and mass

Classical mechanics

Newton’s first law of motion, inertia and mass

Newton’s first law appears simple at first look, but has far-reaching consequences that shape physics and define its two important ideas — those of mass and inertia. In this article we will examine Newton’s first law and its implications.

To many, Newton’s thee famous laws seem too trivial to be iconic. Yet, these form the basis of physics applicable in everyday life (often termed classical physics). The key factor one needs to understand here is why these laws are important on the timeline of physics: they signify one of the earliest applications of mathematics to physics and they stand as one of the earliest examples of a scientific approach taken to answer a question.

These three laws speak about the world around us, specifically, how things move — the dynamics of bodies. In this article, we will be taking a look at Newton’s first law. You can always browse through our Learn section for more.

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Newton’s first law

Newton’s first law describes inertial frames of reference by asserting their existence. This is why it is also known as the law of inertia. However, this definition is not clear directly from the statement of the law:

An object at rest stays at rest, and an object in motion remains in motion with a uniform velocity, unless acted upon by an unbalanced force.

We can split the law into three clauses:

  1. An object at rest remains at rest
  2. An object in motion remains in motion at a constant speed, in a constant direction
  3. These states of rest or motion can only be disrupted by an unbalanced force

An unbalanced force is one with no neutralising effect. For instance, a force of x units northwards needs a force of units southwards or perhaps two forces of (x/√2) units each, southeastwards and southwestwards, and so on, to balance it out. Should such a balancing factor not exist, we call the existing force an unbalanced force.

(We have already discussed vectors and scalars; if your understanding is rusty, now would be a good time to learn about them briefly.)

Inertia and mass

All this tells us about the habit of everything in this universe is that they adamantly remain in their present state. More scientifically, this tells us how an object prefers to retain its state of rest or motion so long as some unbalanced force does not disturb it. This preference, or resistance of an object to any change in its state of rest or motion is termed inertia.

This was a powerful idea because in Newton’s time it was largely believed that objects preferred to come to rest. Nobody bothered about a force like friction that they could not see, so to speak. (Newton would talk about another invisible force that he called “gravity” later on.)

However, the idea of friction must rightly be attributed to Galileo who believed that such a force existed and worked towards bringing moving things to rest. It is interesting how Galileo arrived at his idea.

Galileo inertia experiment 1

From fig. 1 it is clear that an object released at position A on some container would reach position B at the same height as A — under ideal circumstances.

Galileo inertia experiment 2

From fig. 2, Galileo modified his experiment and found that this height would be reached regardless of the angle of inclination, i.e. no matter how wide or narrow the container got.

Galileo inertia experiment 3

From fig. 3, the genius of Galileo shows: he reasoned that if the angle was a full 180 degrees, the object should keep moving, never being able to attain its desired height. Yet, in practicality, the object stops. So, he reasoned, there must be some force stopping it; a force we now call inertia.

So much for inertia. Now think of the individuality of an object: do some have more inertia? In other words, do some have a greater preference to remain at rest or motion? The answer is simply that they do, and this degree of preference that an object has to remain at its present state is given the term mass. Mass is also defined, when more convenient, as the amount of matter contained in a body; but it is more scientifically described as the measure of the tendency of an object to oppose a change in its state of rest or motion.

Mass, in other words, is a measure of inertia of an object.

Inertial frames of reference

There is a catch to this law. Consider a bowling ball rolling along a polished wooden floor on a ship. The ball keeps rolling until some force stops it. This force could be friction with the floor, collision with a wall etc. Assuming the floor is perfectly polished (frictionless) we realise that the ball keeps moving at a uniform velocity.

Suppose the ship (and hence the entire room) was accelerating away from some point, then the bowling ball would, with respect to that point, no longer have a constant velocity — not because of any change in direction, but because of a change in speed due to acceleration — thereby rendering Newton’s law invalid.

It is important to note, therefore, that the fact that this law can be experimentally verified tells us that frames of reference exist (such as our bowling room in the last example) wherein this law remains true. Such frames are called inertial frames of reference and hence this statement is called the law of inertia. Frames where this law does not apply are called non-inertial reference frames.

Newton's first law inertia

What would happen if those ropes got cut?
Image courtesy, D. Sinclair Terrasidius

Newton’s first law in everyday life

The law of inertia has a huge number of experimental verifications in daily life. Consider the way you fall forwards or backwards when a car brakes to a halt or accelerates at a traffic light. That is due to inertia, when your body would rather remain moving forwards than slow to a halt, or vice versa.

The same is true when making a turn. You tend to lean leftwards when turning right because  your body would rather continue in a straight line forwards, which, when you turn left is now on your right. Similarly, you fall left when turning right.

It is for the same reason that you would have a nasty fall if you let go of a fast-moving swing in the park. Although the fall and the path you take before your face hits the ground are governed by other forces, the reason why you leave your chair on the swing and fly into the air is due to inertia.

Although not direct, the ideas that this law introduces go on to become pivotal in framing physics, from rotational dynamics to cosmology, the concepts of mass and inertia play a role almost everywhere. This discussion, however, is beyond the scope of this article, simply to maintain simplicity.

In the next article we will talk about Newton’s second law, acceleration, impulse and momentum.

 

Cover image from Wikimedia Commons.

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V.H. Belvadi is an Assistant Professor of Physics. He teaches postgraduate courses in advanced classical mechanics, astrophysics and general relativity. When he is free he makes photographs and short films, writes on his personal website, makes music, reads voraciously, or plays his violin. He currently serves as the Editor-in-Chief of Physics Capsule.

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