Measurement of Length and Motion -Notes

Measurement is the process of finding out the size, length, or amount of something using standard units. Measurement is a fundamental aspect of science. It allows scientists to quantify observations, compare results, and communicate findings with accuracy and consistency. Precise measurement guarantees that we can communicate quantities with definite numbers in an effective manner. Modern technology has shifted the techniques of measurement from body parts ( like foot, arm length) to many scales and machines. Without measurement, you will only get inaccurate and incomplete results in most of the daily tasks. For example, imagine you have used your entire hands to sprinkle some salt over food instead of a spoon. The taste will be spoiled. It is almost impossible to build houses, manufacture products without accurate measurement.

History of measurement

India has a rich and ancient tradition of measurements, which evolved through trade, construction, astronomy, and daily life. Indian measurement systems were highly advanced even in prehistoric times, and many of them were remarkably precise for their era.

1. Indus Valley Civilization (c. 2600–1900 BCE) Steatite (stone) weights: Cubical and standardized in a binary or decimal system. Rulers were used . Rulers were divided into units as small as 1.7 mm, indicating great precision.
2. Vedic Period (c. 1500–500 BCE) the measurement was based on the body parts. Angula (finger's breadth), Dhanusha (bow's length),Hasta (forearm length) were in use. Yojana (distance measure, ~12–15 km). Units like Ratti was used in weighing gems. Nimisha (blink of an eye), Muhurat (~48 minutes) and Yuga (cosmic age) were used to measure time.
3. During the Mauryan Period (c. 321–185 BCE) Kautilya’s Arthashastra (by Chanakya) has defined the units of land as Nivartana, KulyavapaKarsha, Pala, Tula as units of weight.
4. During the medieval Period (c. 700–1700 CE) Sultans and Mughal rulers introduced new systems. They continued use of Tola (11.66 grams), Ser, Maund (around 37 kg). Akbar Introduced the Ilahi Gaj (royal yardstick) AND used Gaz, Bigha, and Dham for land measurement.
5. During British Period (1757–1947 CE) the Imperial system (inches, pounds, miles) were introduced. Indian traditional units were gradually replaced by modern tools and techniques.
6. After the independence Era (1947–present) a standard metric System has been in use. Units like Meter, kilogram, liter, etc.are used. However, some traditional units like tola (used for gold) are still popular culturally and commercially.

Measurement Using Body Parts

In ancient times, people commonly used body parts such as hand spans, arm lengths, and foot lengths for measuring objects and distances. Though not precise, these units were practical for everyday tasks.

Unit	Description	Approximate Modern Equivalent
Angula	Width of a finger	~1.75 cm
Hasta	Distance from elbow to tip of middle finger (forearm)	~45 cm
Dhanusha	Length of a bow (used in warfare and rituals)	~1.8 m
Yard	Distance from nose to fingertip of an outstretched arm	~91.4 cm
Foot	Length of the human foot	~30.5 cm
Cubit	Distance from elbow to the tip of the middle finger	~45 to 52 cm
Span	Distance between thumb and little finger when fully extended	~20 cm
Pace	A full step taken while walking	~75 cm to 1 m
Hand	Width of a palm (used to measure height of horses)	~10 cm

Use of our body parts for measurement is not a great idea. Each of us have different lengths, heights, weights which gives inconsistent results. This variation can lead to inaccuracies and confusion. The table below shows reasons for inaccuracies while using body parts for measurement

Disadvantages of Using Body Parts for Measurement

S.No.	Disadvantage	Explanation
1.	Inaccuracy	Body sizes vary from person to person, leading to inaccurate measurements.
2.	Lack of Standardization	No fixed or universally accepted values for units like foot, cubit, etc.
3.	Difficult to Reproduce	The same measurement may differ when repeated by different people.
4.	Unsuitable for Large Distances	Measuring large areas or distances is impractical using body parts.
5.	Not Precise Enough	Cannot achieve fine or scientific accuracy required in engineering or science.
6.	Variation with Age and Growth	Children and adults have different body sizes, affecting measurement values.
7.	Regional Differences	The same unit (e.g., cubit) had different lengths in different cultures/regions.
8.	Prone to Misuse or Cheating	Can be manipulated in trade or deals to benefit one party unfairly.

Standard Units / The Metric System (SI Units – International System of Units)

As the world became more connected, people realized that using different local systems of measurement created confusion. To overcome this, a global standard called the International System of Units (SI units) was introduced. Most countries now use the Metric System, a decimal-based system used in science and everyday life.

Quantity	SI Unit (Metric)	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin (Celsius in daily use)	K(degree C)
Electric Current	Ampere	A
Luminous Intensity	Candela	cd
Amount of Substance	Mole	mol

Measuring Large and Small Lengths

Type of Length	Unit	Symbol	Used To Measure	Example
Very Small Lengths	Millimeter	mm	Thickness of a coin, insect size	Thickness of a paper ~ 0.1 mm
	Nanometer	nm	Molecules, light wavelengths	Wavelength of visible light ~500 nm
	Small Lengths	Centimeter	cm	Pencil, book, small objects	Width of a finger ~ 2 cm
		Inch (Imperial)	in	Screen size, tools	Smartphone screen ~ 6 in
Medium Lengths	Meter	m	Height, room size, athletics	100 meter race
Large Lengths	Kilometer	km	Road distances, travel	Distance between cities
	Mile (Imperial)	mi	Long road distances (in US/UK)	1 mile ~ 1.6 km
Very Large Lengths	Megameter	Mm	Used in geology, astronomy	Earth's diameter ~ 12.7 Mm
	Light Year	ly	Distance light travels in one year	Nearest star ~ 4.2 ly
	Astronomical Unit	AU	Average Earth to Sun distance	1 AU ~149.6 million km
	Parsec	pc	Stellar distances in astronomy	1 parsec ~ 3.26 light years

Conversion Between Units / Unit Conversion Table

1. Length Conversion

From ? To	Multiply By	Example
1 kilometer (km)	= 1000 m	5 km = 5000 m
1 meter (m)	= 100 cm	2 m = 200 cm
1 centimeter (cm)	= 10 mm	3 cm = 30 mm
1 inch	= 2.54 cm	4 in = 10.16 cm
1 foot (ft)	= 30.48 cm	6 ft = 182.88 cm
1 mile	= 1.609 km	2 miles = 3.218 km

2. Mass (Weight) Conversion

From ? To	Multiply By	Example
1 kilogram (kg)	= 1000 g	2 kg = 2000 g
1 gram (g)	= 1000 mg	5 g = 5000 mg
1 pound (lb)	= 0.4536 kg	10 lb = 4.536 kg
1 ounce (oz)	= 28.35 g	3 oz = 85.05 g

3. Time Conversion

From ? To	Multiply By	Example
1 minute	= 60 seconds	2 min = 120 s
1 hour	= 60 minutes	1 hr = 60 min
1 day	= 24 hours	1 day = 1440 min
1 week	= 7 days	2 weeks = 14 days

5. Volume Conversion

From ? To	Multiply By	Example
1 liter (L)	= 1000 mL	2 L = 2000 mL
1 milliliter (mL)	= 1 cm cube	5 mL = 5 cm cube
1 US gallon	= 3.785 L	2 gal = 7.57 L
1 cup (US)	= 240 mL	3 cups = 720 mL

Correct Way of Measuring Length

Step	Action	Why It is Important
Use the Right Measuring Tool	Use a ruler, measuring tape, meter scale, or Vernier caliper depending on the length.	Different tools are suited for different sizes and required accuracy.
Place Object on a Flat Surface	Keep the object and scale on a level surface.	Prevents errors due to tilt or misalignment.
Align with Zero Mark	Always begin measuring from the zero mark on the scale.	Ensures the full and correct length is measured.
View from Eye Level	Keep your eye directly above the measurement mark.	Avoids parallax error (false reading due to viewing angle).
Read Closest Mark	Note the marking at the point where the object ends.	Gives you the correct length.
Record Units Clearly	Always include the unit with the measurement (e.g., cm, mm, m).	Prevents misunderstanding or errors in interpretation.

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

If the zero mark (beginning) or final end of the scale is broken or unclear, you can still measure length accurately by following this correct method.

1. Start from a Clear Mark (e.g., 1 cm or 5 cm) . Place one end of the object aligned with a known, undamaged mark (e.g., 1 cm instead of 0 cm).
2. Note the Starting Reading. Let’s say you start from 1.0 cm.
3. Note the Ending Reading. Suppose the other end of the object reaches 15.3 cm.
4. Subtract to Find Actual Length. Suppose, measured Length = Ending Reading – Starting Reading.
5. Measured Length = 15.3 cm – 1.0 cm = 14.3 cm

How Visually Challenged Students Measure Lengths

Visually challenged (blind or low-vision) students can also learn and perform measurements using special tools, techniques, and tactile methods. These tools are designed to be felt through touch or read with assistive features like Braille. Here's how they measure lengths effectively:

Tool	Description
Braille Ruler	A ruler with raised tactile markings and Braille numbers, allowing measurement by touch.
Tactile Tape Measure	A flexible tape with raised divisions and either Braille or high-contrast, large-print numbers for easier identification.
Tactile Calipers	Used to measure thickness or diameter, these calipers have tactile notches or clicking mechanisms for precise readings.
Tactile Geometry Tools	Special compasses, protractors, and rulers designed with raised edges and feedback to allow safe, tactile exploration of geometric shapes.

Writing Units of Length correctly

When writing units of length, it's important to follow standard rules to avoid confusion. Here's a guide to help write them properly: 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. .For example; 12 cm, 3.5 m is correct but the incorrect is 12cm, 3.5m.

Measuring the Length of a Curved Line

Measuring a curved line (like the edge of a leaf or the path of a river on a map) is different from measuring a straight line. Here's how you can do it:

Method: Using a Divider and a Ruler

This is a common method used in schools.

Steps:

1. Take a divider (a geometry tool with two pointed legs).
2. Adjust the divider to a small, fixed length (e.g., 1 cm).
3. Place one point of the divider at the starting point of the curve.
4. Step along the curve using the divider, marking each step.
5. Count how many steps it took to reach the end of the curve.
6. Multiply the number of steps by the length between the divider’s legs.

Example:
If the divider was opened to 1 cm and it took 12 steps to cover the curved line:
Length of curve = 12 × 1 cm = 12 cm

Alternative Method: Using a Thread

A flexible method for irregular curves.

Steps:

1. Take a non-stretchable thread or string.
2. Place the thread along the entire length of the curved line, carefully following the curve.
3. Mark the points where the curve starts and ends on the thread.
4. Straighten the thread and measure it with a ruler.

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.

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.

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

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

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

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.

Key Concepts

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

QUESTION ANSWERS

Question 1. Some lengths are given in Column I of the following Table. Some units are given in Column II. Match the lengths with the units suitable for measuring those lengths.

COLUMN-1	COLUMN-2
Distance between Delhi and Lucknow	centimetre
Thickness of a coin	kilometre
Length of an eraser	metre
Length of school ground	Millimetre

Answer:

COLUMN-1	COLUMN-2
Distance between Delhi and Lucknow	kilometre
Thickness of a coin	millimetre
Length of an eraser	centimetre
Length of school ground	metre
Distance between Delhi and Lucknow	kilometre

Question 2. Read the following statements and mark True (T) or False (F) against each.
(i) The motion of a car moving on a straight road is an example of linear motion.
Answer: True

(ii) Any object that is changing its position concerning a reference point with time is said to be in motion.
Answer: True

(iii) 1 km = 100 cm
Answer: False

Question 3. Which of the following is not a standard unit of measuring length?
(i) millimetre
(ii) centimetre
(iii) kilometre
(iv) handspan
Answer: (iv) handspan

Question 4. Search for the different scales or measuring tapes at your home and school. Find out the smallest value that can be measured using each of these scales. Record your observations in a tabular form.

Answer:

Scale/Measuring Tape	Location	Smallest Value Measured
Ruler	Home/School	1 mm
Measuring Tape	Home/School	1 mm or 1 cm (depending on the type)
Metre Stick	School	1 cm
Vernier Caliper	School Lab	0.1 mm
Micrometer (Screw Gauge)	School Lab	0.01 mm
Digital Caliper	School	0.01 mm

Question 5. Suppose the distance between your school and home is 1.5 km. Express it in metres.
Ans.
∵ 1 km = 1000 metres
∴ 1.5 km = 1.5 × 1000
= 1500 metres

Question 6. Take a tumbler or a bottle. Measure the length of the curved part of the base of the glass or bottle and record it.
Answer: Hint: Use a flexible measuring tape or a piece of string to measure the length of the curved part of the base of the tumbler, then measure the string against a ruler.

Question 7. Measure the height of your friend and express it.
(i) metres
(ii) centimetres and
(iii) millimetres.
Answer:
Hint: Measure the height using a metre scale and express it in:

• Metres (e.g., 1.4 m)
• Centimetres (e.g., 140 cm)
• Millimetres (e.g., 1400 mm)

Question 8. You are given a coin. Estimate how many coins are required to be placed one after the other lengthwise, without leaving any gap between them, to cover the whole length of the chosen side of a notebook. Verify your estimate by measuring the same side of the notebook and the size of the coin using a 15-cm scale.

Answer:

• Number of coins = (Notebook Length) / (Coin Diameter)
• Number of coins = 18 cm / 2 cm = 9
  Measure the diameter of the coin and the length of the notebook. Divide the length of the notebook by the diameter of the coin to estimate the number of coins required. Say the diameter of the coin is 2 cm and the length of the notebook is 18 cm. Then = 9 coins can be placed side to side along the length of the notebook. Verify by placing the coins end-to-end and measuring again.

Question 9. Give two examples each for linear, circular, and oscillatory motion.
Answer:

• Linear motion: A car moving on a straight road, an eraser dropping straight down.
• Circular motion: A merry-go-round, the motion of a whirling stone tied to a thread.
• Oscillatory motion: A swinging pendulum, the motion of a metal strip pressed and released.

Question 10. Observe different objects around you. It is easier to express the lengths of some objects in mm, some in cm, and some in m. Make a list of three objects in each category and enter them in the following Table.

Unit of Measurement	Objects
Millimeters (mm)	Thickness of a coin, Thickness of a cardboard, Diameter of a small screw
Centimeters (cm)	Length of a pencil, Width of a book, Height of a water bottle
Meters (m)	Height of a room, Width of a playground, Height of a lamppost

Question 11. A roller coaster track is made in the shape shown in Fig. A ball starts from point A and escapes through point F. Identify the types of motion of the ball on the rollercoaster and corresponding portions of the track.

Roller Coaster Track

Answer: Portions of the track and corresponding types of motion:

• A to B: Linear motion
• B to C: Circular motion (loop)
• C to D to E: Circular motion
• E to F: Linear motion

Question 12. Tasneem wants to make a metre scale by herself. She considers the following materials for it – plywood, paper, cloth, stretchable rubber, and steel. Which of these should she not use and why?
Answer: Tasneem should not use stretchable rubber because it can change length when stretched, leading to inaccurate measurements. Plywood, cloth, paper, and steel are more suitable as they maintain consistent lengths.

Question 13. Think, design, and develop a card game on conversion of units of length to play with your friends.
Answer: Create cards with different lengths and corresponding units (mm, cm, m, km). Each card can have a length in one unit and players must match it to its equivalent in another unit. For example, a card with “100 cm” would match with “1 m”.