CBSE Class 6- Science Chapter 5: Measurement of Length and Motion- Study Notes (PDF)

Study Notes: Measurement of Length and Motion (Class 6-NCERT(Curiosity) Science

1. The Need for Standard Measurement

The process of measurement involves comparing an unknown quantity with a known, fixed quantity called a unit. A measurement is expressed in two parts: a number and the unit. For example, “13 handspans” consists of the number 13 and the unit “handspan.”

1.1 Non-Standard Units and Their Limitations

Historically and informally, people have used various parts of the body or familiar objects as units of measurement. These are known as non-standard units.

• Examples from the NCERT text-book:
  • char angula (four fingers width)
  • Length of the arm
  • Strides or length of feet
  • handspan (also called balisht)
• The Core Problem: Non-standard units, like handspans, are not consistent. They differ from person to person because body parts vary in size.
• Demonstration in the text: When Deepa and her friends (Anish, Hardeep, Padma, Tasneem) measured their classroom table using their handspans, they all recorded different numbers (ranging from slightly less than 13 to 14), demonstrating the unreliability of this method for consistent results.

1.2 Ancient Indian Measurement Systems

Ancient Indian literature mentions several units of measurement used in architecture, town planning, and by traditional craftspeople.

• Units Mentioned: Angula (finger width), dhanusa, and yojana.
• Archaeological Evidence: Scales with ruled markings have been discovered at Harappan Civilisation sites, indicating a long history of systematic measurement in India.

2. Standard Units of Measurement

To overcome the confusion and inconsistency of non-standard units, countries worldwide adopted a uniform system.

• The International System of Units (SI Units): This is the globally accepted system of standard units.
• SI Unit of Length: The SI unit for length is the metre (m).

2.1 Metric System Subdivisions and Multiples

The metre is the base unit, but for measuring very large or very small lengths, other related units are more convenient.

• Kilometre (km): Used for large distances, such as between cities.
  • 1 km = 1000 m
• Centimetre (cm): A smaller division of a metre. A standard 15-cm scale is a common tool.
  • 1 m = 100 cm
• Millimetre (mm): An even smaller division, representing the smallest value that can typically be measured on a standard school scale.
  • 1 cm = 10 mm
  • 1 mm = 0.1 cm
• Other Units: The text also mentions older units like the inch and foot, which are still in use.
  • 1 inch = 2.54 cm

3. Correct Techniques for Measuring Length

Accurate measurement requires not just a standard unit but also proper technique.

3.1 Choosing the Right Tool

• For straight lines: A 15-cm scale is suitable for small objects like a pencil, while a metre scale is better for a room’s height.
• For curved lines or surfaces: A flexible measuring tape (like a tailor’s tape) is necessary for measuring the girth of a tree or a person’s chest.

3.2 Proper Placement and Reading

• Scale Placement: The scale must be placed in direct contact with the object, running along its length.
• Eye Position: To avoid parallax error, the eye must be positioned directly above the marking being read. Viewing from an angle can lead to an incorrect reading.
• Using a Broken Scale: If the zero mark is unclear or the end is broken, start the measurement from another full mark (e.g., 1.0 cm). To find the length, subtract the starting reading from the final reading (e.g., 10.4 cm – 1.0 cm = 9.4 cm).

3.3 Measuring a Curved Line

A curved line cannot be measured with a rigid scale.

• Method: Use a flexible tool like a thread. Place the thread along the curved line, marking the start and end points. Then, straighten the thread and measure its length against a standard metre scale.

4. Describing Position and Motion

4.1 The Concept of a Reference Point

To describe the location or position of an object, it must be stated in relation to a fixed object or point.

• Reference Point: A fixed point from which distances are measured.
• Example: Students discussing the distance to a garden had different opinions because they were each using their own house as a reference point. If they had all used a common reference point, like the bus stand, their observations would have been consistent. Kilometre stones on a highway use a destination city (e.g., Delhi) as the reference point.

4.2 Defining Motion and Rest

• Motion: An object is in motion if its position changes with time with respect to a reference point.
• Rest: An object is at rest if its position does not change with time with respect to a reference point.
• Relativity of Motion: Whether an object is in motion or at rest depends entirely on the chosen reference point. For example, passengers on a moving bus are at rest relative to the bus itself, but they are in motion relative to a tree or building outside.

5. Types of Motion

Objects can move in different ways, which are classified into several types.

• Linear Motion: Motion along a straight line.
  • Examples: A car on a straight road, an orange falling from a tree, students in a march-past.
• Circular Motion: Motion along a circular path.
  • Examples: A stone whirled on a thread, a merry-go-round.
• Oscillatory Motion: Repetitive to-and-fro movement about a fixed position.
  • Examples: A child on a swing, an eraser hung from a thread and released, the vibrating end of a metal strip.
• Periodic Motion: Any motion that repeats its path after a fixed interval of time. Both circular and oscillatory motions are types of periodic motion.

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Quiz

Short-Answer Questions (25 Questions)

(Answer in 2-3 sentences.)

1. What are the two essential parts of any measurement?
2. Why did Deepa and her friends get different measurements for the same table when using their handspans?
3. Name two ancient Indian units of length mentioned in the text.
4. What is the International System of Units (SI units) and why was it adopted?
5. What is the SI unit of length and what is its symbol?
6. How many centimetres are in one metre, and how many millimetres are in one centimetre?
7. For what kind of measurements is a kilometre a more convenient unit than a metre?
8. Why is a flexible measuring tape more suitable than a rigid metre scale for measuring the size of your chest?
9. Describe the correct way to place a scale when measuring the length of an object.
10. Explain why your eye’s position is important when reading a scale. What is this type of error called?
11. How can you accurately measure an object using a scale with a broken zero mark?
12. Describe the method for measuring the length of a curved line using a thread.
13. What is a reference point and why is it important for describing an object’s position?
14. Using the example from the text, explain why the students had different opinions about whether the school or the garden was closer.
15. What do the kilometre stones on a highway, such as ‘Delhi 70 km’, indicate?
16. Define what it means for an object to be in “motion”.
17. Define what it means for an object to be “at rest”.
18. Explain how passengers on a bus can be considered both at rest and in motion simultaneously.
19. What is linear motion? Provide one example from the text.
20. What is circular motion? Provide one example from the text.
21. What is oscillatory motion? Provide one example from the text.
22. What is periodic motion?
23. Which two types of motion discussed are also considered periodic?
24. According to the text, how do visually challenged students measure lengths?
25. What are the rules for writing the symbols for units like metre (m) and kilometre (km)?

Multiple-Choice Questions (20 Questions)

1. Which of the following is an example of a non-standard unit of measurement? a) Metre b) Centimetre c) Handspan d) Kilometre
2. What is the SI unit of length? a) Centimetre b) Kilometre c) Metre d) Millimetre
3. How many metres are in one kilometre? a) 10 b) 100 c) 1000 d) 10,000
4. The motion of a child on a swing is an example of: a) Linear motion b) Circular motion c) Oscillatory motion d) All of the above
5. To measure the girth of a tree, the most appropriate tool would be a: a) 15-cm scale b) Metre scale c) Flexible measuring tape d) Metal rod
6. An object is said to be at rest if its position does not change with time with respect to a: a) Moving object b) Reference point c) Circular path d) Different observer
7. A car moving on a straight road is demonstrating: a) Circular motion b) Oscillatory motion c) Periodic motion d) Linear motion
8. How many millimetres are in one centimetre? a) 10 b) 100 c) 1000 d) 1
9. If you measure a pencil starting at the 2.0 cm mark and the tip ends at the 14.5 cm mark, what is the length of the pencil? a) 14.5 cm b) 16.5 cm c) 12.5 cm d) 12.0 cm
10. The motion of a merry-go-round is classified as: a) Linear b) Oscillatory c) Circular d) Random
11. What is the term for a fixed object or point from which distances are stated? a) Start point b) Origin c) Reference point d) Base unit
12. The problem with using units like angula or strides is that they: a) Are too small b) Are not internationally recognized c) Differ from person to person d) Cannot be used for curved lines
13. The motion of an eraser whirled at the end of a string is: a) Linear b) Circular c) Oscillatory d) At rest
14. Which of the following statements is FALSE? a) 1 km = 1000 m b) 1 m = 100 cm c) 1 cm = 10 mm d) 1 km = 100 cm
15. Both circular motion and oscillatory motion are considered to be: a) Linear b) Periodic c) Constant d) Non-standard
16. One inch is equal to: a) 1.54 cm b) 2.54 cm c) 3.54 cm d) 10 mm
17. To avoid parallax error when reading a scale, your eye should be: a) To the left of the mark b) To the right of the mark c) Directly above the mark d) As far away as possible
18. In ancient India, the term angula referred to: a) Arm length b) Finger width c) A single stride d) A type of scale
19. An orange falling from a tree moves along a: a) Circular path b) Straight line c) Oscillatory path d) Curved path
20. When writing a measurement, what should be between the number and the unit symbol? a) A full stop b) A hyphen c) A space d) Nothing

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Answer Keys

Short-Answer Questions – Answer Key

1. The two essential parts of any measurement are a number and a unit. For example, in “13 handspans,” 13 is the number and “handspan” is the unit.
2. They all got different measurements because the size of a handspan is a non-standard unit that varies from person to person. Their hands were of different sizes, leading to inconsistent results for the table’s length.
3. Two ancient Indian units of length mentioned are angula (finger width) and yojana. Others like dhanusa are also mentioned.
4. The SI units are a standardized set of measurement units adopted by countries to avoid confusion. This system ensures that a measurement of a quantity is the same regardless of who measures it or where it is measured.
5. The SI unit of length is the metre. Its symbol is a lowercase ‘m’.
6. There are 100 centimetres in one metre (1 m = 100 cm). There are 10 millimetres in one centimetre (1 cm = 10 mm).
7. The kilometre is more convenient for measuring larger lengths or distances, such as the length of a railway track or the distance between two cities.
8. A flexible measuring tape is more suitable because it can bend to follow the curved surface of a chest. A rigid metre scale cannot be bent and would not provide an accurate measurement.
9. The scale should be placed in direct contact with the object, positioned along the entire length that is being measured.
10. Your eye should be positioned directly above the scale marking to get an accurate reading. Viewing from an angle can cause a parallax error, making the measurement appear different from its actual value.
11. You can start the measurement from any other clear, full mark on the scale, such as 1.0 cm. Then, subtract this starting reading from the reading at the other end to find the object’s true length.
12. To measure a curved line, first lay a thread exactly along the path of the line. Then, straighten the thread and measure its length against a standard metre scale.
13. A reference point is a fixed point used to describe the position of an object. It is important because position and motion are relative, and a common reference point ensures that descriptions of location are consistent and unambiguous.
14. The students had different opinions because they were each using their own house as a reference point. The distance to the school and garden was different from each of their houses.
15. The kilometre stones indicate the distance from a specific reference point. ‘Delhi 70 km’ means the location of the stone is 70 kilometres away from the reference point, which is Delhi.
16. An object is in motion if its position changes with respect to a reference point over time.
17. An object is at rest if its position does not change with respect to a reference point over time.
18. Relative to a reference point inside the bus (like their seat), the passengers are at rest. However, relative to a reference point outside the bus (like a building on the street), their position is changing, so they are in motion.
19. Linear motion is motion along a straight line. An example is an orange falling from a tree or students in a march-past.
20. Circular motion is motion along a circular path. An example is a merry-go-round or an eraser being whirled at the end of a thread.
21. Oscillatory motion is the to-and-fro movement of an object about a fixed position. An example is a child on a swing.
22. Periodic motion is any type of motion where an object repeats its path after a fixed interval of time.
23. Both circular motion and oscillatory motion are considered periodic because they repeat their movements over and over.
24. Visually challenged students use scales with raised markings. They can feel these markings by touching them to determine lengths.
25. The symbols (km, m, cm, mm) should be written in lowercase letters. They are not followed by ‘s’ for plural, and a full stop is not used after the symbol unless it is at the end of a sentence.

Multiple-Choice Questions – Answer Key

1. c) Handspan
2. c) Metre
3. c) 1000
4. c) Oscillatory motion
5. c) Flexible measuring tape
6. b) Reference point
7. d) Linear motion
8. a) 10
9. c) 12.5 cm (14.5 – 2.0 = 12.5)
10. c) Circular
11. c) Reference point
12. c) Differ from person to person
13. b) Circular
14. d) 1 km = 100 cm
15. b) Periodic
16. b) 2.54 cm
17. c) Directly above the mark
18. b) Finger width
19. b) Straight line
20. c) A space

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Essay Questions and Answers ( For Teachers)

Q1. Discuss the evolution from non-standard to standard units of measurement as presented in the text. Why was this transition necessary for trade and communication?

Answer: The text illustrates the evolution of measurement by first introducing non-standard units, which are based on convenient but inconsistent measures like body parts. Examples include the handspan (balisht), char angula (four fingers width), arm’s length, and strides. The core problem with these units, as demonstrated when the children measured a table, is their variability; since everyone’s hand or stride is a different size, measurements are not reproducible or reliable. This inconsistency created confusion, especially as people began to travel and trade between different regions. To facilitate clear communication, trade, and scientific collaboration, a uniform system was necessary. This led to different countries coming together to adopt a set of standard units, known as the International System of Units (SI). The SI unit for length, the metre, provides a fixed, unchanging standard that ensures a measurement of “one metre” is the same everywhere in the world, solving the problem of ambiguity and enabling precision in all fields.

Q2. Explain the concept of a “reference point” and its critical role in defining both position and motion. Use the examples of the students discussing the garden and Padma’s bus journey to support your explanation.

Answer: A reference point is a fixed object or point from which the distance to another object is measured to describe its position. The text highlights its importance by showing that without a common reference point, descriptions of position can be contradictory. For instance, Deepa and her friends all had different, yet correct, ideas about whether the school or the garden was closer because they were each using their own house as a unique reference point. If they had all used a single reference point, such as the bus stand, their conclusions about the distances would have been the same. This concept is equally critical for defining motion. An object is only in motion if its position is changing with respect to a reference point. In Padma’s bus journey, the kilometre stones use Delhi as the reference point. The changing numbers on the stones (from ‘Delhi 70 km’ to ‘Delhi 60 km’) indicate that her position relative to Delhi is changing, which means she is in motion towards it. This shows that motion is not absolute but is always described relative to a chosen reference point.

Q3. Describe the three main types of motion discussed in the text: linear, circular, and oscillatory. For each type, provide its definition and two distinct examples mentioned or depicted in the source material.

Answer: The text classifies motion into three primary types:

Linear Motion: This is defined as motion along a straight line. One example is the march-past of students during a parade, where they move in a straight path. Another example is an orange falling from a tree, which moves directly downwards in a straight line towards the ground.

Circular Motion: This is defined as motion along a circular path. One example provided is a merry-go-round in a park, where the riders move in a circle. Another example is a child whirling an eraser tied to a thread, causing the eraser to move in a circular path.

Oscillatory Motion: This is defined as a repetitive to-and-fro movement about a fixed position. A primary example is a child on a swing, who moves back and forth. Another example is the motion of the free end of a metal strip that has been pressed down and released, causing it to vibrate up and down.

Q4. Detail the proper procedures for measuring length accurately with a scale, addressing potential challenges like parallax error and a broken scale. Why are these procedures important?

Answer: To measure length accurately, several procedures must be followed. First, the scale must be placed in direct contact with the object, along its length. Second, to avoid parallax error, the observer’s eye must be positioned directly above the mark on the scale being read; viewing from an angle can make the measurement appear shorter or longer than it actually is.

The text also addresses challenges. If a scale has a broken end or an unclear zero mark, one should not guess the starting point. Instead, the measurement should begin at a clear, subsequent full mark, like 1.0 cm. The final length is then calculated by subtracting this starting reading from the end reading (e.g., if it ends at 10.4 cm, the length is 10.4 – 1.0 = 9.4 cm). These procedures are crucial because they ensure that measurements are not only accurate but also consistent and repeatable, which is the fundamental goal of using a standard measurement system.

Q5. Explain the concept of the relativity of motion using the scenario of Deepa on the bus. How can an object be simultaneously at rest and in motion?

Answer: The relativity of motion means that an object’s state of motion (or rest) depends entirely on the observer’s frame of reference, or the chosen reference point. The text perfectly illustrates this with Deepa on the bus. When Deepa considers the bus itself as her reference point, she observes that the other passengers are not changing their position relative to her or their seats. From this perspective, the passengers are at rest.

However, when Deepa looks outside and chooses a building on the side of the road as her reference point, she sees that the passengers’ (and her own) position is constantly changing. From this external perspective, the passengers are in motion. Therefore, an object can be simultaneously at rest and in motion because its status is defined relative to different reference points.

Q6. Compare and contrast the metric units of length: millimetre, centimetre, metre, and kilometre. Explain the hierarchical relationship between them and provide an example of an object or distance best measured by each.

Answer: The metric units of length presented—millimetre (mm), centimetre (cm), metre (m), and kilometre (km)—are part of a hierarchical system based on multiples of 10, which makes conversions straightforward. The metre is the base SI unit. The other units are convenient for measuring objects of vastly different scales.

Relationship: 1 kilometre = 1000 metres; 1 metre = 100 centimetres; 1 centimetre = 10 millimetres.

Millimetre (mm): This is the smallest unit discussed, best for measuring very small lengths with precision. An example would be the thickness of a single coin or a page of a book.

Centimetre (cm): This unit is suitable for small, everyday objects. Examples include the length of a pencil or an eraser.

Metre (m): This is the standard unit, ideal for larger objects and short distances. Examples include the length of a classroom table or the height of a room.

Kilometre (km): This largest unit is used for measuring long distances. The most prominent example from the text is the distance between two cities, such as Delhi and Lucknow.

Q7. What is periodic motion? Explain how both circular and oscillatory motions can be classified as periodic, using examples for each.

Answer: Periodic motion is defined as any motion where an object repeats its path after a fixed interval of time. It is characterized by its repetitive nature.

Circular Motion as Periodic: An object in circular motion, such as a horse on a merry-go-round, continuously travels along the same circular path. After each full rotation, it returns to its starting point and repeats the journey. This regular repetition makes it a form of periodic motion.

Oscillatory Motion as Periodic: An object in oscillatory motion, like a child on a swing, moves back and forth about a central fixed position. This to-and-fro movement is repeated over and over again in a regular time interval. Because the motion is repetitive, it is also classified as periodic.

Q8. Imagine you are teaching a younger student how to measure a curved line, like the arch of a verandah. Based on the text, write out a clear, step-by-step set of instructions for them to follow.

Answer: To measure a curved line like an arch, you can’t use a straight ruler. Here is a simple, step-by-step guide:

Get Your Tool: Find a piece of non-stretchy thread or string that is longer than the arch you want to measure.

Align the Thread: Carefully place one end of the thread at the very beginning of the arch. Hold it firmly in place with your finger.

Trace the Curve: Lay the thread down so it follows the exact curve of the arch. Make sure the thread is flat against the surface and follows all the bends.

Mark the End: Once the thread has covered the entire length of the arch, mark the spot on the thread that lines up with the end of the arch. You can pinch it with your fingers or make a small mark with a pen.

Measure the Thread: Now, pick up the thread and pull it straight. Use a standard metre scale or measuring tape to measure the length of the thread from its starting end to the mark you made. This length is the measurement of the curved arch.

Q9. Describe the experiment conducted by Deepa and her friends to measure the classroom table. What was the unit of measurement, what were the results, and what was the ultimate conclusion drawn from this activity?

Answer: Deepa and her friends decided to measure the length of their classroom table. The unit of measurement they chose was a non-standard unit: their own handspan, which Deepa’s mother called a balisht. Each of the five students—Anish, Padma, Tasneem, Deepa, and Hardeep—measured the table and recorded their results. The results, as shown in Table 5.1, were all different: Padma measured 13 handspans, Hardeep measured 14, Anish measured slightly more than 13, Tasneem measured slightly less than 13, and Deepa measured between 13 and 14. The ultimate conclusion they drew from this experiment was that their measurements differed because their handspans were all of different sizes. This led them to understand the unreliability of non-standard units and appreciate why standard tools like scales and measuring tapes are necessary for consistent and accurate measurement.

Q10. A rollercoaster ball travels along a track as shown in Figure 5.19. Based on the principles in the text, identify the different types of motion (linear and circular) the ball would experience as it moves along different portions of the track.

Answer: Based on the principles of motion described in the text, the rollercoaster ball would experience different types of motion.

Linear Motion: The ball exhibits linear motion when it moves along a straight line. In Figure 5.19, the portions of the track from point A to B and from point E to F are straight. On these sections, the ball’s motion would be classified as linear.

Circular Motion: The ball exhibits circular motion when it moves along a circular path. The large loop in the track, between points C and D, is a circular path. As the ball travels through this loop, its motion would be classified as circular. The sections from B to C and D to E are curved but not part of a complete circle or straight line, representing a more complex motion not explicitly defined in the text, but the primary loop is clearly circular motion.

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Glossary of Key Terms

Term	Definition
Angula	An ancient Indian unit of measurement corresponding to a finger width.
Balisht	Another term for a handspan, used as a non-standard unit of length.
Centimetre (cm)	A standard unit of length. 100 centimetres make one metre.
Char angula	A measurement equal to four fingers width.
Circular motion	The motion of an object when it moves along a circular path.
Kilometre (km)	A standard unit for measuring large lengths. One kilometre is equal to 1000 metres.
Length	A measurement of distance.
Linear motion	The motion of an object when it moves along a straight line.
Measurement	The process of comparing a quantity with a standard unit. It consists of a number and a unit.
Metre (m)	The SI unit of length.
Millimetre (mm)	A standard unit of length. 10 millimetres make one centimetre.
Motion	An object is said to be in motion if its position changes with respect to a reference point with time.
Oscillatory motion	The motion of an object when it moves to and fro about some fixed position.
Periodic motion	Motion where an object repeats its path after a fixed interval of time.
Reference Point	A fixed object or point with respect to which distance is stated or motion is described.
Rest	An object is said to be at rest if it is not changing its position with respect to the reference point with time.
SI units	The International System of Units, a set of standard units of measurement adopted globally.
Unit	A known, fixed quantity used for measurement.