Chapter Notes: Measurement of Length and Motion

Introduction

Measurement is crucial in our daily lives for various tasks like buying fabric, cooking, or building structures. Accurate measurement ensures that we can communicate quantities effectively and consistently. For instance, if you want to buy fabric to make a dress, you need to know how much fabric is required. Similarly, when following a recipe, precise measurement of ingredients is necessary to get the desired taste and texture. Without measurement, it would be challenging to build houses, manufacture products, or even perform simple tasks like buying groceries.

How do we Measure?

Do you think the length of the bench would be the same if you measured it with different people’s handspans?

How can using a scale or measuring tape help avoid mistakes in measurement?

Measuring using Body Parts

Body parts such as hand spans, arm lengths, and foot lengths were commonly used for measurement in the past.
For example:

• Handspan: The distance from the tip of the thumb to the tip of the little finger when the hand is fully stretched.
• Arm Length: The distance from the shoulder to the tip of the middle finger.
• Foot Length: The length of a person’s foot can also be used to measure things.
• Stride: Farmers sometimes use their steps or strides to measure lengths for dividing their fields.

Arm length, food length & Handspan

Issues with Non-Standard Units

• Using body parts for measurement has a significant drawback: it is not uniform. Since people’s body parts vary in size, the same length can be measured differently by different individuals. This variation can lead to inaccuracies and confusion. 
• For example, if you and your friend both measure a table using your foot lengths, you might get different results because your feet are not the same size. This inconsistency highlighted the need for standard units of measurement.

Ancient Indian Measurement Systems

• India has a long history of measurement systems that go back to ancient times. Units like Angula (which is the width of a finger), Dhanusa, and Yojana were used in ancient Indian literature for measuring things like artifacts, buildings, and town layouts. 
• The Angula is still used today by traditional workers such as carpenters and tailors. Archaeologists have even found objects with markings, possibly scales, at Harappan Civilization sites, showing the use of these ancient measurements.

Try yourself:

Which of the following is a drawback of using body parts for measurement?

• A.Inconsistency in measurement due to variations in body sizes.
• B.Increased accuracy in measurements.
• C.Standardization of units.
• D.Ease of communication.

View Solution

Standard Units

Over time, different parts of the world developed their own systems of measurement. However, as people began to travel more, these varied systems caused confusion. To solve this, countries came together and agreed on a standard set of units known as the International System of Units, or SI units.

The SI Unit of Length: Metre

• The SI unit for measuring length is called the metre, and its symbol is m.
• A metre is divided into 100 equal parts, each called a centimetre (cm).
• For example, a standard 15-cm ruler has markings from 0 to 15 cm. The distance between each number is 1 cm.
  A 15-cm scale
• Each centimetre is further divided into 10 smaller parts, called millimetres (mm). One millimetre is equal to 0.1 cm, making it the smallest length you can measure with a regular ruler.

Measuring Large and Small Lengths

• To measure larger distances, we use a unit called a kilometre (km), which is equal to 1000 metres.
• For smaller lengths, we use units like centimetres or millimetres.
• Examples:
  • If you measure the length of your pencil and find it to be 15 cm, that means it is 15 times the length of one centimetre.
  • If the distance between two cities is 20 km, that means it is 20,000 metres long.

Conversion between Units

It is important to know how to convert between different units of length:

• 1 metre = 100 centimetres
• 1 centimetre = 10 millimetres
• 1 kilometre = 1000 metres

Measuring Length in Inches

On some rulers, you may see another set of markings labeled in inches. One inch is equal to 2.54 centimeters. In the past, units like inches and feet were commonly used to measure length, and some people still use these units today.

Correct Way of Measuring Length

Different scales are used for different lengths. For example:

• To measure the length of a pencil, a 15-cm ruler is ideal.
• If you need to measure the height of a room, a metre stick or measuring tape works best.
• To measure around something like a tree trunk or your chest, a flexible measuring tape, like the one used by tailors, is more appropriate.

What is the correct way to place the scale?

• The scale should be placed in contact with the object along its length. 
• For example, if you are measuring the length of a paper, place the scale so that it touches the paper along its entire length.
  Method of placing the scale

What is the correct position of the eye while reading the scale?

• The eye should be directly above the point of measurement to avoid parallax error, which can lead to incorrect readings. 
• For example, if you are measuring the length of a pencil, your eye should be directly above the point where the pencil meets the scale.Correct position of the eye is ‘B’

How to measure the length if the ends of the scale are broken?

• If the ends of a scale are broken, you can still use it for measurement. Use any other full mark on the scale as the starting point. The reading at the end of the object is then subtracted from this mark to find the length. 
• For example, if you start at the 1 cm mark and measure to 10 cm, the length of the object is 10 cm – 1 cm = 9 cm.
  Correct method of placing the scale with broken end

How Visually Challenged Students Measure Lengths

• Visually challenged students measure lengths by using special scales with raised markings. 
• These markings can be felt by touch, allowing them to accurately measure without needing to see the scale.

Writing Units of Length Correctly

• When writing units of length like kilometre, metre, centimetre, and millimetre, the names and their symbols (km, m, cm, mm) always start with lowercase letters, except at the beginning of a sentence. 
• The symbols should never have an “s” added for the plural, and no full stop is placed after the symbol unless it’s at the end of a sentence. Also, remember to leave a space between the number and the unit when writing the length.

Measuring the Length of a Curved Line

Curved lines can be measured using a flexible measuring tape or a thread. Wrap the thread along the curve, then straighten the thread and measure its length using a metre scale. 

Try yourself:

Which unit of length is equal to 1000 meters?

• A.Centimeter
• B.Kilometer
• C.Millimeter
• D.Inch

View Solution

Describing Position

A reference point is a fixed point used to describe the position of an object. It provides a basis for comparison. For example, when giving directions, you might use a landmark as a reference point, such as “the park is two blocks north of the school.”

Examples of Reference Points in Real Life

• The starting line in a race
• The kilometre stones on a highway
• A landmark such as a building or a tree

Importance of Consistent Reference Points

• Using consistent reference points ensures that measurements and descriptions of positions are accurate and comparable. 
• For example, if everyone uses the same reference point when describing the location of a place, it eliminates confusion and ensures clarity.

Moving Things

What makes you think an object is moving or not?

What’s a fun way to check if a toy is in motion or not?

Motion and Rest of an Object

An object is considered to be in motion if its position changes over time relative to a fixed reference point. If the object’s position does not change with respect to the reference point over time, it is said to be at rest.

Types of Motion

1. Linear Motion

Linear motion occurs when an object moves along a straight line. The direction of motion doesn’t change, and the object continues along the same straight line. The speed and direction might change, but the path remains a straight line.
Examples include:

• A car driving on a straight road
• An athlete running a 100-meter dash
• A train moving on straight tracks
  Linear motion

2. Circular Motion

Circular motion occurs when an object moves along a circular path. In this type of motion, the object constantly changes direction as it keeps moving along the curve, always staying the same distance from a central point. The path is not straight, but curved in the shape of a circle.
Examples include:

• The motion of a merry-go-round
• The hands of a clock
• A satellite orbiting the Earth

Circular motion

3. Oscillatory Motion

Oscillatory motion occurs when an object moves to and fro about a fixed position. The motion repeats itself in regular intervals, with the object moving to one side, then back to the other, and repeating this cycle over and over again. The path of the motion is not linear or circular but swings between two points.
Examples include:

• The motion of a swing
• The vibration of a guitar string
• The movement of a pendulum
  Oscillatory motion

Periodic Motion: Circular and Oscillatory

• An object is said to be in periodic motion if it repeats its path after a fixed interval of time. In circular motion, an object moves along the same circular path repeatedly. 
• Similarly, in oscillatory motion, an object moves back and forth in a repeating pattern. Both circular and oscillatory motions are examples of periodic motion.

Try yourself:

Which type of motion occurs when an object moves along a straight line?

• A.Linear motion
• B.Circular motion
• C.Oscillatory motion
• D.Periodic motion

View Solution

Key Concepts

• Measurement is essential for accuracy and consistency in various tasks.
• Traditional Methods of measurement using body parts were inconsistent.
• Standard Units of Measurement like the metre provide a uniform way of measuring.
• Different scales are used for different lengths, and proper techniques ensure accurate measurements.
• Reference Points are essential for describing positions and determining motion.
• Objects can be classified as in motion or at rest based on their position relative to a reference point.
• Motion can be linear, circular, or oscillatory, each with distinct characteristics and examples.