## Table of Contents

## Inertia

**Inertia** is the property of a mass which resists change from its state of rest or motion.

- The inertia of an object refers to the reluctance of the object to start moving if it is stationary in the first instance or the reluctance of the object to stop moving if it is moving in the first instance.
- When a body of matter is stationary, it needs a force to make it start moving. The bigger the mass, the bigger the force needed. We say that masses have inertia: a reluctance to start moving.

In other words, the larger the mass of an object, the harder it will be for the object to:

- start moving;
- slow down;
- move faster; or
- change direction.

Inertia is also the reason behind the importance of wearing seat belts in vehicles. When a driver abruptly applies the brakes, their forward motion persists due to inertia. Without a seat belt restraining them, they would collide with the windshield. A seat belt supplies the required opposing force to bring them to a halt and prevent injury.

## Mass

The mass (m) of a body of matter is quantitative measure of its inertia, i.e., its resistance to a change in the state of rest or motion of the body, when a force is applied.

- SI unit of mass is the kilogram
^{1}(kg). It is a scalar quantity. - The greater the mass of a body, the smaller the rate of change in motion.

### Note On Mass

Matter is the material substance that constitutes the observable universe and, together with energy, forms the basis of all objective phenomena. The basic building blocks of matter are atoms. The atoms themselves comprise of nucleus and electrons.

## Amount Of Substance

Although mass is defined in terms of inertia, it is conventionally interpreted as:

The mass (m) of a body of matter is a measure of its amount of substance in the body.

- Under ordinary circumstances, matter does not change. Hence, the amount of substance in the body can be assumed to be quantitatively equal to its mass. If the amount of substance divides itself, we can assume that its mass also halved.
- Mass can be measured with a beam balance or an electronic balance.

**Note: **As you might recall in Base quantities, the base SI unit for amount of substance is mol.

## Footnotes

- The kilogram, established as the standard unit of mass, was historically defined until 2019 as the mass of a platinum–iridium alloy stored at the Office of Weights and Measures in Paris. In May 2019, the International System of Units (SI) underwent a significant redefinition, and the kilogram was redefined based on the Planck constant rather than a physical object. This redefinition ensures a more stable and universally applicable standard for mass measurement. The Planck constant is measured using sophisticated experimental techniques such as the Kibble balance, which compares mechanical power and electrical power to determine the constant’s value with extraordinary precision. ↩︎

## Worked Examples

### Example 1: Understanding Inertia

A 5 kg bowling ball and a 0.2 kg tennis ball are placed on a frictionless surface. If the same force is applied to both balls, which one will have a greater acceleration, and why?

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According to Newton’s second law, acceleration ($a$) is directly proportional to force ($F$) and inversely proportional to mass ($m$), $a = \frac{F}{m}$. Given that the same force is applied to both balls, the ball with the smaller mass (the tennis ball) will have a greater acceleration. This is because the tennis ball has less inertia, or resistance to changes in its state of motion, compared to the bowling ball.

### Example 2: Mass and Inertia

A truck and a car are moving at the same speed on a highway. If both need to stop abruptly, which one will require a greater stopping force, and why?

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The truck will require a greater stopping force because it has a greater mass than the car. A greater mass means greater inertia, or a greater resistance to changes in its state of motion, including stopping. Thus, more force is needed to overcome the inertia of the truck to bring it to a stop.

### Example 3: Seat Belts and Inertia

Explain why wearing a seat belt is an effective safety measure using the concept of inertia.

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When a vehicle abruptly stops, the inertia of the passengers makes them continue moving forward at the original speed of the vehicle. Without a seat belt, passengers would continue moving forward until an external force stops them, potentially leading to injury by colliding with the windshield or other parts of the vehicle’s interior. A seat belt provides the necessary force to counteract the passengers’ inertia, restraining them and bringing them to a stop more safely and at the same rate as the vehicle.

### Example 4: Mass Measurement

If you have a beam balance and need to measure the mass of a substance that is expected to be divided later, how would the division of the substance affect its measured mass?

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The division of the substance would proportionally reduce its mass. Since mass is a measure of the amount of substance, dividing the substance into smaller portions would result in each portion having a correspondingly smaller mass. For example, if the substance is initially measured to have a mass of 10 kg and is then divided equally into 2 parts, each part would have a mass of 5 kg. This is because the amount of substance and thus the mass is halved.

### Example 5: Inertia’s Role in Everyday Life

Describe an everyday situation where inertia plays a critical role and explain the physics behind it.

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One common situation is when you abruptly stop when running. Your feet stop moving, but the upper part of your body continues moving forward due to inertia. This is because your body’s mass resists the change in its state of motion. To stop without falling, you must lean backward or take a step forward to counteract your forward motion. This example illustrates how inertia affects motion and the necessity of applying a counteracting force to change the state of motion safely.