# Physics Tutorial: Newton's First Law of Motion. The Meaning of Inertia

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In this Physics tutorial, you will learn:

• The definition of Newton's First Law of Motion
• The meaning of balanced and non-balanced forces
• The meaning of inertia and its relationship with mass
• The scientific definition of mass based on the concept of inertia
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4.5Newton's First Law of Motion. The Meaning of Inertia

## Introduction

Think about the following questions:

1. Can a moving object be in equilibrium of forces? Why?
2. What about objects at rest? Are they in equilibrium?
3. How can we distort the equilibrium of forces acting on an object? Explain.

These questions and other like these are answered within this Physics tutorial so please read carefully

## What does Newton's First Law of Motion State?

As stated in the Physics tutorial "What Causes the Motion? The Meaning of Force", forces are the only factors that cause motion. Therefore, all the three Newton's Laws we will discuss in the next tutorials deal with forces, despite being called "Newton's Laws of Motion".

In the abovementioned tutorial, it was also stated that when an object is at rest, it means there is an equilibrium of forces acting on it. For example, a book resting on a table is under the effect of two opposite forces:

1. Gravitational force, Fg, which causes the object to weigh on the table and
2. Normal force, N, which is a kind of resistive force produced by the table against any possible deformation caused by the book's weight.

These two forces are equal in magnitude and opposite in direction. Look at the figure below:

Therefore, it is obvious that when the resultant force acting on an object at rest is zero, the object will continue to remain at rest. (1)

On the other hand, when we discussed the concept of terminal velocity in the Physics tutorial "Types of Forces II. Resistive Forces (Frictional Force. Drag). Terminal Velocity", we stated that starting from the moment when the sum of resistive forces (frictional force plus air drag) become equal to the moving force (i.e. when the resultant force acting on the moving object becomes zero), the object will move at constant velocity, whose magnitude is equal to the last velocity before the equilibrium was established. We called this constant velocity as "terminal velocity".

Therefore, we can say when the resultant force acting on a moving object becomes zero, it will continue moving at constant velocity. (2)

It is obvious that if no force is acting on the object, the resultant force on it, can be taken as zero. Therefore, the lack of acting forces on an object represents a special case of equilibrium.

Hence, we say when no force is acting on the object, it will maintain its previous state of uniform motion, i.e. if it was at rest, will continue to be at rest and if it was moving, it will continue moving at constant velocity. (3)

Combining the statements (1), (2) and (3), we obtain the definition of Newton's First Law of Motion. It states that:

"If no force is acting on an object or when the resultant of all forces acting on it is zero, the object will still be at rest if initially it was at rest or it will continue moving at constant velocity (at terminal velocity) if initially it was moving."

When the resultant force at an object is zero, we say, "the forces acting on it are balanced, otherwise, they are unbalanced."

### Example 1

In which of the following scenarios the Newton's First Law of Motion is being applied? For simplicity, take g = 10 N/kg in all cases.

1. A 2 kg stone is falling downwards. The magnitude of air drag is equal to 16.3 N.
2. A 2000 kg car is moving along a horizontal plane of friction coefficient equal to 0.7. Air resistance is 1400 N and the driving force is equal to 15400 N.
3. A submarine moves underwater by means of a 20500 N driving force. Air resistance if it was moving above the water would be 2000 N while the actual water drag is 20500 N.

### Solution 1

a. The only forces acting on the falling stone are the gravitational force, Fg (acting downwards) and air resistance (drag) D, which acts upwards, as the air tries to show resistance to the motion.

If we take the gravitational force as positive, then the air drag will be negative. We have

FR = Fg + D

Since

Fg = m × g = 2 kg × 10 N/kg = 20 N

we obtain

FR = 20 N + (-16.3) N = 3.7 N

Since the resultant force is not zero, there is no equilibrium. As a result, forces are unbalanced. This means Newton's First Law of Motion is not being applied in this case.

b. The situation is described in the figure below.

Let's calculate the frictional force first. We take it as negative (like the air drag) because it acts in the opposite direction of motion. Hence, we have

f = -μ × N
= -μ × m × g
= -0.7 × 2000 kg × 10 N/kg
= -14000 N

The vector equation of the forces acting on the car is

FR = F + f + D

where F is the driving (moving) force. Substituting the known values, we obtain for the magnitude of the resultant force:

|FR| = 15400N - 14000N - 1400N
= 0

This result means the forces are balanced. As a result, the Newton's First Law of Motion is applied in this case.

c. The figure below shows the horizontal forces acting at the submarine. (In the vertical direction, the weight is balanced by the buoyant [or lifting] force of water).

Since the driving force is equal to the water drag (20500 N each) and giving that they are in opposite directions, there is equilibrium of forces at the submarine. Air resistance is not considered here as it acts outside the water. Therefore, the Newton's First Law is applied in this case.

## The Meaning of Inertia

One of the conclusions drawn by observing the Newton's First Law of Motion, is that all objects tend to preserve their previous state of motion. This property is known as Inertia. Thus, we say an object is very inert if we have difficulty in changing its actual state of motion. Let's illustrate this point with some examples.

1. An avalanche is very dangerous as it takes away everything on its way during its downhill motion. Therefore, we say an avalanche is very inert as it is quite impossible to stop it. Indeed, may people have died when an avalanche has taken them away when moving at snowy mountains.
2. It is very easy to make a balloon move and also to stop it when it is moving. Therefore, we say the balloon is not very inert.
3. When you are standing inside a bus and it immediately stops, your equilibrium is distorted as for few seconds you move in the previous direction of bus motion. This occurs because your body possesses some inertia and therefore, it tends to preserve its previous state of motion. The same thing occurs when the bus starts moving immediately. In this case, your body goes backward as it tries to stay at rest as it was before.

From the above examples, it is clear that inertia is a quantity related to the mass of objects. Thus, greater the mass of an object, higher its inertia, i.e. the tendency to preserve the previous state of motion.

In fact, scientifically, the mass is identified and defined through the concept of inertia. We have given a definition regarding mass in the Physics tutorial "Length, Mass and Time. Dimensional Analysis" where it was stated that "Mass is the quantity of matter a body contains". However, this definition is not scientifically correct, i.e. it is a very simplified definition of mass, which interferes with the scientific definition of the quantity of matter measured in mole (remember, mole is a fundamental SI unit). Therefore, the definition of mass provided in in the abovementioned tutorial represents a simplified version, used for an easy understanding of this physical quantity.

In scientific terms, we say, Mass represents a quantitative measure of Inertia, which is a fundamental property of all matter. Therefore, a 100 kg object is 100 times more inert than a 1 kg object as it is 100 times more difficult to make a 100 kg object move (or stop when it is moving) than a 1 kg one.

### Example 2

Which of the objects or situations written inside the brackets is more appropriate for the required action?

1. To keep a door opened when there is a lot of wind blowing (barbell, chair)
2. To score a goal with your own head during a football match (bowling ball, soccer ball)
3. To drink a coffee during a trip (inside a moving car, while walking)
4. To stop a downhill moving car when its brakes are not working (one man using his own hands, four men using a fishing net)

### Solution 2

1. The action (keeping a door opened) requires a high inertia to avoid the door's crash because of the wind. Therefore, a barbell is more appropriate than a chair for this purpose, as the barbell is heavier and is more helpful in keeping the door in the actual position.
2. Bowling ball is too heavy (massive) than soccer ball, i.e. it has a very high inertia. Therefore, it is not suitable to make a header with a bowling ball as it may cause harm on your head. Soccer ball is better in this regard.
3. It is better do drink a coffee while walking than while travelling in car because you walk at low velocity and in case of stoppage, the coffee doesn't spill out of the cup, unlike in the car.
4. When a car is moving downhill in an uncontrollable manner, it is better to avoid staying on its way, especially when there is only one person who is trying to stop the car. You must try to gather as many people as possible instead and try to make a soft stop of the car through a fishing net or anything similar, to avoid damages caused by the car's high inertia.

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