Measurement of Length and Motion
Complete student notes with internal links, definitions, charts, diagrams, textbook solutions and interactive quiz.
1. Chapter Overview
This chapter explains how length is measured, why standard units are needed, how to measure correctly, how to describe position using a reference point, and how to identify motion and different types of motion.
2. Important Definitions Chart
| Term | Definition |
|---|---|
| Measurement | The process of comparing an unknown quantity with a known fixed quantity called a unit. |
| Length | The distance between two points or the measure of how long an object is. |
| Unit | A fixed quantity used as a standard for measurement. |
| Standard Unit | A unit accepted and used everywhere so that measurements remain uniform. |
| SI Units | The International System of Units used as standard units of measurement. |
| Metre | The SI unit of length. Its symbol is m. |
| Centimetre | A smaller unit of length. 1 m = 100 cm. |
| Millimetre | A still smaller unit of length. 1 cm = 10 mm. |
| Kilometre | A larger unit of length used to measure long distances. 1 km = 1000 m. |
| Reference Point | A fixed point or object with respect to which the position or distance of another object is described. |
| Motion | An object is in motion if its position changes with respect to a reference point with time. |
| Rest | An object is at rest if its position does not change with respect to a reference point with time. |
| Linear Motion | Motion of an object along a straight line. |
| Circular Motion | Motion of an object along a circular path. |
| Oscillatory Motion | To-and-fro motion of an object about a fixed position. |
| Periodic Motion | Motion that repeats its path after a fixed interval of time. |
| Justification | A reason or explanation given to support an observation or answer. |
3. How Do We Measure?
In earlier times, people used body parts such as handspan, foot, arm length, finger width and stride to measure length. For example, angula means finger width, and balisht means handspan.
| Traditional Unit | Meaning | Problem |
|---|---|---|
| Handspan / Balisht | Distance between the tip of thumb and little finger when the hand is stretched. | Different people have different handspans. |
| Foot length | Length of a person’s foot. | Foot size differs from person to person. |
| Stride | Length of one step while walking. | Stride length depends on the person. |
| Angula | Finger width used in ancient Indian measurement systems. | Finger width is not the same for everyone. |
4. Standard Units of Length
The system of units now used worldwide is known as the International System of Units or SI units. The SI unit of length is metre, and its symbol is m.
| Unit | Symbol | Used For | Relation |
|---|---|---|---|
| Kilometre | km | Long distances like distance between cities | 1 km = 1000 m |
| Metre | m | Length of room, school ground, height of a person | 1 m = 100 cm |
| Centimetre | cm | Length of pencil, eraser, notebook | 1 cm = 10 mm |
| Millimetre | mm | Thickness of coin, page, small objects | 10 mm = 1 cm |
Correct Way to Write Units
- Write unit symbols in lowercase: km, m, cm, mm.
- Do not add “s” after unit symbols. Write 5 cm, not 5 cms.
- Leave a space between number and unit. Write 10 cm, not 10cm.
- Do not put a full stop after the unit symbol unless it is at the end of a sentence.
5. Correct Way of Measuring Length
To measure accurately, we must choose a suitable measuring device and use it correctly.
| Situation | Correct Method | Reason |
|---|---|---|
| Measuring a pencil | Use a 15-cm scale and place it along the length of the pencil. | The scale must be in contact with the object. |
| Measuring height of a room | Use a metre scale or measuring tape. | A small ruler is not convenient for large lengths. |
| Measuring chest size or tree girth | Use a flexible measuring tape. | Curved surfaces need flexible measuring devices. |
| Reading the scale | Keep the eye exactly above the mark to be read. | This avoids reading errors due to wrong eye position. |
| Broken zero mark | Start from another full mark, such as 1 cm, and subtract the initial reading. | Length = final reading − initial reading. |
6. Measuring the Length of a Curved Line
A straight ruler cannot directly measure a curved line. To measure a curved line, we can use a flexible measuring tape or a thread.
Method Using Thread
- Take a thread and place it carefully along the curved line.
- Mark the starting and ending points on the thread.
- Straighten the thread without stretching it.
- Measure the length of the marked part using a scale.
7. Describing Position and Reference Point
To describe the position of an object, we need a fixed point or object. This fixed point is called a reference point.
| Situation | Reference Point | Position / Distance Description |
|---|---|---|
| Kilometre stone says “Delhi 70 km” | Delhi | The person is 70 km away from Delhi. |
| Drawing Kabaddi court | A fixed point on the ground | All lines are drawn by measuring from that point. |
| Distance of school and garden | Each student’s house or bus stand | Different reference points can give different observations. |
8. Motion and Rest
An object is said to be in motion if its position changes with respect to a reference point with time. If its position does not change with respect to a reference point with time, it is said to be at rest.
| Object / Situation | Reference Point | Motion or Rest? | Reason |
|---|---|---|---|
| Passengers sitting inside a moving bus | The bus | At rest | Their position does not change with respect to the bus. |
| Same passengers | A building outside the bus | In motion | Their position changes with respect to the building. |
| Tree | Ground | At rest | Its position does not change with time. |
| Cow grazing in field | Tree or pole in field | In motion | Its position changes with time. |
9. Types of Motion
The chapter discusses three important types of motion: linear motion, circular motion and oscillatory motion.
| Type of Motion | Meaning | Examples |
|---|---|---|
| Linear Motion | Motion along a straight line. | Falling eraser, marching students, car on a straight road, box pushed straight. |
| Circular Motion | Motion along a circular path. | Merry-go-round, whirling eraser tied to thread, rotating fan blade, wheel of a bicycle. |
| Oscillatory Motion | To-and-fro motion about a fixed position. | Swing, pendulum, vibrating metal strip, see-saw movement. |
| Periodic Motion | Motion that repeats after a fixed interval of time. | Circular motion and oscillatory motion are usually periodic. |
10. Difference Between Important Topics
| Topic 1 | Topic 2 | Difference |
|---|---|---|
| Non-standard Units | Standard Units | Non-standard units such as handspan and foot vary from person to person. Standard units such as metre and centimetre remain the same everywhere. |
| Metre | Kilometre | Metre is used for medium lengths. Kilometre is used for long distances. |
| Centimetre | Millimetre | Centimetre is used for small lengths. Millimetre is used for very small lengths like thickness of a coin. |
| Rigid Scale | Flexible Measuring Tape | A rigid scale is used for straight objects. A flexible tape is used for curved surfaces like chest size or tree girth. |
| Motion | Rest | In motion, position changes with time with respect to a reference point. At rest, position does not change with time with respect to a reference point. |
| Linear Motion | Circular Motion | Linear motion is along a straight path. Circular motion is along a circular path. |
| Circular Motion | Oscillatory Motion | Circular motion follows a circular path. Oscillatory motion is to-and-fro about a fixed position. |
| Reference Point | Position | A reference point is a fixed point used for comparison. Position tells where an object is with respect to that reference point. |
11. Quick Revision Points
- Measurement means comparing a quantity with a unit.
- Body-based units like handspan and foot are not reliable because they differ from person to person.
- SI unit of length is metre, symbol m.
- 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- Choose a suitable measuring device for accurate measurement.
- Keep the scale in contact with the object along its length.
- Keep the eye directly above the reading mark.
- If zero mark is broken, subtract initial reading from final reading.
- Use a thread or flexible tape to measure curved lines.
- A reference point is needed to describe position and motion.
- An object is in motion if its position changes with respect to a reference point with time.
- An object is at rest if its position does not change with respect to a reference point with time.
- Linear motion is motion along a straight line.
- Circular motion is motion along a circular path.
- Oscillatory motion is to-and-fro motion about a fixed position.
- Circular and oscillatory motions are periodic in nature.
12. Textbook Question Answers
1. Match the lengths with suitable units.
| Length | Suitable Unit |
|---|---|
| Distance between Delhi and Lucknow | Kilometre |
| Thickness of a coin | Millimetre |
| Length of an eraser | Centimetre |
| Length of school ground | Metre |
2. Mark True or False.
(i) The motion of a car moving on a straight road is an example of linear motion. True
(ii) Any object which is changing its position with respect to a reference point with time is said to be in motion. True
(iii) 1 km = 100 cm. False. Correct relation: 1 km = 1000 m = 100000 cm.
3. Which is not a standard unit of measuring length?
Answer: Handspan is not a standard unit because its length differs from person to person.
4. Search for different scales or measuring tapes and find the smallest value measured by each.
Answer: This is an activity-based question. A sample answer is given below.
| Measuring Device | Smallest Value It Can Measure | Common Use |
|---|---|---|
| 15-cm scale | 1 mm | Pencil, eraser, small objects |
| Metre scale | 1 mm or 1 cm depending on markings | Desk, room height, board length |
| Tailor’s tape | 1 mm or 1 cm depending on markings | Body measurements and curved surfaces |
| Measuring tape used in sports | 1 cm | Ground, court or long distances |
5. Distance between school and home is 1.5 km. Express it in metres.
Answer: 1 km = 1000 m
1.5 km = 1.5 × 1000 m = 1500 m
6. Measure the length of the curved part of the base of a tumbler or bottle.
Answer: Use a thread or flexible measuring tape. Place the thread around the curved base, mark the complete length, straighten the thread and measure it using a scale. The measured value is the length of the curved part.
7. Measure the height of your friend and express it in metres, centimetres and millimetres.
Answer: This is an activity-based question. Suppose your friend’s height is 1.45 m.
In metres: 1.45 m
In centimetres: 1.45 × 100 = 145 cm
In millimetres: 145 × 10 = 1450 mm
8. Estimate how many coins are required to cover one side of a notebook. Verify by measurement.
Answer: First estimate the number of coins by placing coins mentally along the notebook side. Then measure the length of the notebook side and the diameter of one coin using a scale.
Formula: Number of coins = Length of notebook side ÷ Diameter of coin.
For example, if notebook side = 24 cm and coin diameter = 2 cm, then number of coins = 24 ÷ 2 = 12 coins.
9. Give two examples each of linear, circular and oscillatory motion.
| Type of Motion | Examples |
|---|---|
| Linear Motion | Car moving on a straight road, fruit falling from a tree |
| Circular Motion | Merry-go-round, wheel of a moving bicycle |
| Oscillatory Motion | Swing, pendulum of a clock |
10. List objects whose lengths are easier to express in mm, cm and m.
| Size | Objects |
|---|---|
| mm | Thickness of coin, thickness of notebook page, diameter of pencil lead |
| cm | Length of eraser, length of pencil, width of notebook |
| m | Height of door, length of room, length of school ground |
11. Identify the types of motion of a ball on the rollercoaster track.
Answer: On straight portions of the track, the ball shows linear motion. On curved or loop portions, the ball shows circular motion or motion along a curved path.
Possible classification: AB and EF are linear parts. The loop or curved parts around C, D and E show circular motion.
12. Tasneem wants to make a metre scale. Which materials should she not use and why?
Answer: She should not use cloth and stretchable rubber because they can stretch or bend, causing wrong measurements. Paper is also not ideal because it can tear, fold or get damaged easily. Steel and plywood are better because they are more rigid and stable.
13. Design a card game on conversion of units of length.
Answer: Make two sets of cards. One set contains values like 1 m, 2 km, 5 cm, 10 mm. The other set contains equivalent values like 100 cm, 2000 m, 50 mm, 1 cm. Players must match equivalent cards. The player who makes the maximum correct pairs wins.
13. Interactive Quiz
Choose the correct answer and click submit to check your score.
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