Measurement of Length and Motion

A cloth seller uses a measuring rod, while a tailor uses a flexible tape. Both compare a length with a unit. A measurement has two parts: a numerical value and a unit, such as 2 m. A bare number does not tell another person how long the object is.

Handspan, foot length, arm length and stride can give rough estimates. But people have different-sized hands and feet. The same table may take different numbers of handspans without its length changing. A larger handspan needs fewer repetitions to cover that table.

Standard units provide a shared basis for comparison. They remove the ambiguity of whose hand or foot was used; they do not eliminate mistakes in placement or reading.

Historical context

NCERT mentions angula (finger width), dhanusa and yojana in Indian measurement traditions, and ruled objects excavated at Harappan sites that could have served as scales. These examples do not establish one fixed modern conversion for every historical use. A person’s foot length must also not be confused with a standardised unit called the foot.

The SI unit of length is the metre, written m. Choose a convenient unit for the size: kilometres for distances between cities, metres for a room or ground, centimetres for an eraser and millimetres for a coin’s thickness. Changing the unit changes the number, not the physical length.

On the illustrated classroom ruler, each centimetre is divided into ten equal intervals. One such interval is 1 mm, or 0.1 cm. Inspect the actual divisions on your instrument; not every scale has identical markings.

Write the symbols km, m, cm and mm in lowercase, with a space after the number: 15 cm. Symbols do not take a plural s or an abbreviation full stop. Some rulers also show inches; use the intended scale consistently. One inch equals 2.54 cm.

Activity 5.1 asks you to measure familiar objects and compare results. Choose an instrument with suitable length, shape and divisions. A rigid ruler suits a straight pencil; a flexible, non-stretching tape suits body measurements or the girth of a tree.

1. 1

   Check the tool

   Identify the units and smallest marked interval. Use a longer scale or tape for a room. Stretchable rubber is unsuitable for a dependable scale because its unit spacing changes when stretched.

2. 2

   Align the starting point

   Place the scale in contact with the object, along its length rather than slanting across it. Match the first end to the zero mark, not automatically to the ruler’s physical edge.

3. 3

   Look directly above the endpoint

   Keep your eye directly above the mark at the other end. Viewing from the side can shift the apparent alignment: this is a reading error, not a change in the object.

4. 4

   Record and compare

   Write the value and unit, repeat if needed, and compare your technique with another observer’s. Raised-marking scales allow readings by touch. Small differences deserve investigation; a standard unit alone does not guarantee identical readings.

If the zero end is damaged or unclear but the remaining divisions are sound, start at another clear mark. Read both ends and subtract the starting reading from the ending reading. The endpoint number alone is the length only when the starting reading is zero.

In the textbook example, the object begins at 1.0 cm and ends at 10.4 cm. Its length is 10.4 cm − 1.0 cm = 9.4 cm. The diagram is a reading example, not a life-size ruler for measuring your screen.

For a curved line, lay a thread carefully along the curve and mark its two ends. Straighten the marked portion without stretching it and measure it against a scale. A suitable flexible tape can also follow the curve. The straight gap between the endpoints is not generally the length along the curve.

The same idea measures a bottle’s base circumference or the length of decorative lights around an arch. Keep the thread on the intended boundary, without loose loops or tension that stretches it.

Estimate a very thin sheet

A single sheet may be thinner than the ruler’s smallest division. Measure a tightly aligned stack of a known number of sheets, excluding covers, then divide the total thickness by the sheet count. This estimates average sheet thickness; uneven compression and gaps still matter. A numbered page is one side, so count physical sheets carefully.

Connect a wheel to distance

The further-learning task relates distance travelled to wheel turns: distance = outer circumference × number of turns, provided the wheel rolls without slipping. Measure the circumference with thread first. This is a model for reasoning, not an instruction to add a metal strip to a bicycle. The textbook names the Jones Counter as a further research topic.

A reference point is the chosen object or point from which a position or distance is described. Two people may disagree about whether the garden or school is nearer because they are measuring from different houses. Using the same starting point makes their statements comparable.

When marking a sports court, choose a common starting point before laying out measured lines. When a road marker says Delhi 70 km, Delhi is the stated reference destination. A later marker reading Delhi 60 km indicates a smaller remaining distance along that route.

A distance alone does not specify a unique location in every direction. State the route, side or direction when needed. The chapter’s houses and road examples work because their arrangement is already shown.

An object is in motion when its position relative to the chosen reference changes with time. It is at rest relative to that reference when its position does not change. A single snapshot does not establish a change; compare observations over time.

A seated passenger can be at rest relative to a moving bus and in motion relative to a roadside building. These descriptions are compatible because the references differ. Always include the reference when justifying a classification.

Activity 5.2: give a reason

List objects that appear moving or at rest, name the reference, and record what changed over time. For a tree, distinguish its trunk from a moving branch. The windowless-ship prompt asks you to consider what evidence is available when motion is steady and an outside reference cannot be seen.

Linear motion follows a straight path, such as a box pushed straight across the floor or an eraser dropped vertically in the simple classroom demonstration. Circular motion follows a circle, such as an object on a rotating merry-go-round or an eraser whirled at a fixed distance from a held thread end.

Oscillatory motion goes to and fro about a fixed position. A swing, a gently displaced hanging eraser and the free end of a clamped flexible strip illustrate it. A pendulum follows an arc while oscillating; moving on a curved path does not by itself make it a complete circular revolution.

Periodic motion repeats at regular time intervals. The textbook uses repeating circular and oscillatory examples. Keep the timing condition explicit: a circular path alone does not guarantee equal times for successive rounds, and an irregular back-and-forth movement need not be periodic.

Activities 5.3–5.7: observe the specified part

Compare a dropped eraser, a whirled object, a hanging object, a flexible strip and playground equipment. Use a safe, clear area and supervision for demonstrations; avoid sharp metal strips or whirling objects near people. Name the part you follow, describe its path and then ask separately whether its motion repeats regularly.

Use these prompts to explain a method or justify a classification, rather than repeat a glossary. They cover the thirteen end questions and the further-learning investigations.

1. Choose and convert · questions 1–5, 7, 10, 12–13

   Match a city distance, coin thickness, eraser length and ground length to convenient units. Explain why a handspan varies, inspect the smallest divisions of available scales, and convert 1.5 km to metres. Express one height in m, cm and mm without changing the quantity. Explain why a stretching scale fails, and make equivalent conversion pairs for practice.

2. Estimate, then measure · questions 6 and 8

   Measure around a bottle’s base with thread. Estimate how many equal coins laid edge to edge would span a notebook; compare the notebook length with one coin’s diameter, allowing for a partial coin at the end. Gaps or overlaps spoil the comparison.

3. Classify with evidence · questions 2, 9 and 11

   Give two examples for each motion type and name a reference. In the rollercoaster drawing, distinguish the straight entry/exit from the circular loop. A short curved transition is not automatically a full circle, and following a loop once does not prove periodicity.

4. Extend measurement without false precision

   Compare leaf length and breadth from the same tree, keeping the measurement direction consistent; natural variation need not be a ruler error. Design a maze from measured 1 cm and 2 cm segments. Use the same method when recording height over time. Estimate sheet thickness from a stack, and examine historical units or the wheel-turn method without inventing archaeological dates or measurements.

Select an answer, then check its explanation. You can change your choice and try again. Read both the number and the unit, and identify the reference or condition before deciding.