How Does Mass Affect Inertia? Key Concepts with Practical Examples
In our everyday life, we observe that some effort is required to put a stationary object into motion or to stop a moving object. We ordinarily experience this as a muscular effort and say that we must push or hit or pull on an object to change its state of motion. The concept of force is based on this push, hit or pull. Effect of force can only be explained by describing what happens when a force is applied to an object.
Pushing, hitting and pulling of objects are all ways of bringing objects in motion. A body on the ground, when given a small push, does not move forever. Such observations suggest that rest is the “natural state” of an object. This remained the belief until Galileo Galilei and Isaac Newton developed an entirely different approach to understand motion. This article will familiarise you with the relation between mass and inertia, types of inertia with examples and the laws of inertia.
About the Inventor
Galileo Galilei
Galileo Galilei was born on 15 February 1564 in Pisa, Italy and died on 8 January 1642. He has been called the "father of observational astronomy", the "father of modern physics", the "father of scientific method", and the "father of science". His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, inventing an improved military compass and other instruments.
Newton’s First Law of Motion
Isaac Newton put forward a variety of laws which explain why objects move (or don't move) as they do. The laws are known as Newton's law of motion. The first law states that a body in uniform motion remains in uniform motion and a body at rest remains at rest, unless acted on by a non-zero net external force. Newton's first law is called the law of inertia.
The First Law of Motion
Inertia
The principle of inertia and the foundation of the first law were laid down by Galileo. Inertia is an inherent property of all the bodies by virtue of which they cannot change their state of rest or uniform motion along a straight line on their own. Quantitatively, inertia of a body is measured by its mass. Thus, the heavier the body, the greater is its inertia. Thus, inertia is the property of the body due to which body opposes the change of its state. Inertia of a body is measured by mass of the body.
Mass
Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied.
Thus, it is the measure of the quantity of matter that the object contains.
S.I. unit of mass is kilogram (kg).
Relation Between Mass and Inertia
Inertia increases as the mass of an object increases. It is directly proportional to mass, that is, inertia increases with the increase in the mass and decreases with the decrease in the mass. The heavier the body, the greater is the force required to change its state and hence the greater is inertia. The reverse is also true that a lighter body has less inertia.
Types of Inertia with Examples
The inertia of a body is of three types
Inertia of rest
Inertia of motion
Inertia of direction
Inertia of Rest: It is the inability of a body to change its state of rest by itself e.g., a person standing in a stationary bus falls backward when the bus suddenly starts moving.
Inertia of Motion: It is the inability of a body to change its state of uniform motion by itself. e.g., a person getting down a moving bus or train falls forward.
Inertia of Direction: It is the inability of a body to change its direction of motion by itself e.g., when a car suddenly takes a turn, the person sitting inside is thrown in the outward direction.
Solved Examples
1. Which of the following has more inertia: (i) a rubber ball and a stone of the same size? (ii) a bicycle and a train? (iii) a five rupees coin and a one-rupee coin?
Ans: (i) Mass of the stone is more than the mass of the rubber ball as the inertia is directly proportional to mass. The object having heavier mass will have more inertia, that is stone will have more inertia than a rubber ball.
(ii) A train is heavier than a bicycle therefore the train will be having more inertia than bicycle as inertia is directly proportional to mass.
(iii) The mass of one rupee coin is less than the mass of five-rupee coin so as the five-rupee coin is having more mass than one-rupee coins the five-rupee coin will be having more inertia than one rupee coin as mass is directly proportional to inertia.
2. What is the net external force acting on a bus moving at 40 kmph on a straight road?
Ans: A bus travelling on a straight road at 40 kmph is in uniform motion along a straight line. Therefore, the net external force on it is zero.
3. What are the forces acting on a book resting on a table? Why does it stay at rest despite the forces acting on the book?
Ans: The force acting on the book resting on a table are its weight and the normal force of the table on the book. It stays at rest since the weight mg and normal force N balance each other and the net external force acting on the book is zero. Thus, it is at rest and continues to be at rest.
Conclusion
Newton's first law of motion gives the definition of force and the concept of inertia. Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. The mass of an object is a measure of its inertia.
FAQs on Inertia and Mass Explained for Students
1. What is the fundamental difference between mass and inertia?
The fundamental difference is that mass is the amount of matter an object contains, typically measured in kilograms (kg), while inertia is an object's natural resistance to any change in its state of motion. Mass is the quantitative measure of inertia; it is not the same property. An object has mass, and it exhibits inertia because of that mass.
2. How does an object's mass quantitatively affect its inertia?
An object's mass is directly proportional to its inertia. This means a more massive object has greater inertia and requires a larger force to change its state of motion (to start, stop, or turn). For example, a heavy truck has far more inertia than a light bicycle. Quantitatively, if you double an object's mass, you also double its inertia.
3. Can you provide a real-world example explaining the relationship between mass and inertia?
Consider pushing an empty shopping cart versus a full one. The full cart has more mass. You will notice that it is much harder to get the full cart moving from a standstill, and it is also harder to stop it once it's in motion. This increased resistance to changes in motion is its greater inertia, which is a direct result of its greater mass.
4. How does the concept of inertia explain why leaves fall when a tree branch is shaken?
When the branch is shaken vigorously, it is set into motion. However, the leaves, due to their inertia of rest, tend to remain in their original stationary position. This resistance to moving with the branch causes the connection point between the leaf stem and the branch to experience stress, leading to the leaves detaching and falling.
5. Why is mass considered the quantitative measure of inertia?
Mass is considered the measure of inertia because experiments show that the force required to produce a certain acceleration in an object is directly proportional to its mass (F=ma). An object with more mass (more matter) resists changes in motion more strongly. Since inertia is precisely this resistance, an object's mass becomes the reliable and measurable way to determine 'how much' inertia it has.
6. If inertia is a property, why doesn't it have its own unique unit like mass (kg)?
Inertia is a conceptual property describing an object's behaviour, not a fundamental physical quantity that is measured independently. Since an object's mass (measured in kg) perfectly and consistently quantifies this resistive property, there is no scientific need for a separate unit for inertia. We simply use the unit of mass, the kilogram, as the standard measure of an object's inertia.
7. Is it possible for an object to have inertia but no mass?
No, it is not possible for an object to have inertia without having mass. Inertia is an intrinsic property of mass. An object's inertia exists *because* it has mass. Therefore, an object with zero mass, like a photon, would also have zero inertia in this context, even though it possesses momentum.
8. Does an object's inertia depend on its speed or location?
No, within the scope of classical mechanics as per the CBSE syllabus, an object's inertia depends only on its mass. It is an intrinsic property and does not change with speed, location, or whether it is accelerating. A 10 kg ball has the same inertia on Earth as it does on the Moon, and it has the same inertia whether it is at rest or moving at 100 m/s.
