Measurement of Length and Motion
Why This Matters
Think about a normal day.
Your mother buys 2 metres of cloth for a new dress. The tailor measures your shoulders before stitching it. A road sign says “Delhi 60 km”. You take a bus and watch trees rush past the window.
All of this is about two simple things: how long? and is it moving?
To answer “how long”, we measure length. To answer “is it moving”, we study motion.
But here is the interesting part. Long ago, people measured things using their own hands and feet. That caused a lot of confusion. In this chapter you will see why it caused trouble, and why the whole world agreed on one fixed way to measure. You will also learn the correct way to use a scale, and the different ways things can move.
By the end, you will measure things the right way, and you will be able to look at anything around you and say exactly how it is moving.
The Big Idea
To measure something is to compare it with a fixed amount we all agree on. That fixed amount is called a unit. If everyone uses their own hand or foot as the unit, the same object gives different answers — so we use standard units that never change. The world’s standard unit of length is the metre. And once we can measure positions, we can also say whether a thing is moving or at rest: a thing is moving if its position keeps changing with time.
Let’s Break It Down
Why we measure, and why we need standard units
First, what does it even mean to measure?
To measure length means to find how long something is. We do this by comparing it with a known amount. That known amount is the unit.
Here is the idea in one line. A measurement always has two parts: a number and a unit.
For example, “the table is 5 handspans long”. Here 5 is the number and handspan is the unit. A handspan is the distance from the tip of your thumb to the tip of your little finger when your hand is fully open.
That sounds fine. So what is the problem?
Imagine five friends measure the same classroom table using their own handspans. They get five different answers — like 13 handspans, 12 and a half, 14, 13 and a bit, and 12 and three-quarters. How can one table have so many lengths?
The reason is simple. Their hands are not the same size. A tall student has a big handspan. A small student has a small handspan. Figure 5.1 below shows exactly why this happens.
Long ago, people did use body parts to measure — the foot, the finger-width (called angula in ancient India), the length of an arm, and so on. India even has a rich, ancient history of such units. They worked for one person. But they failed the moment two people, or two towns, tried to share a measurement. Whose foot? Whose hand?
So countries came together and agreed on units that are exactly the same everywhere in the world. These are called standard units. The full system is called the International System of Units, or SI units for short.
A standard unit does not change from person to person. One metre is one metre — in your home, in your school, and in another country. That is the whole point.
Let us make sure the reason is crystal clear before moving on.
Why can't we use the handspan as a proper unit for everyone to share?
Because everyone’s handspan is a different size. The same object then gives different numbers to different people. A good unit must be fixed and the same for all — that is why we use standard units like the metre.
Units of length and simple conversions
The standard (SI) unit of length is the metre. Its short symbol is m.
How long is a metre? It is roughly the width of a single door, or the height of a kitchen counter. A cricket pitch is about 20 metres long.
But one unit is not enough for everything. Measuring the thickness of a page in metres would be silly. Measuring the distance between two cities in metres would take forever. So we have a family of units — small ones for small things, big ones for big things.
Here are the four you must know, from smallest to biggest:
- millimetre (mm) — very small, about the thickness of a debit or credit card.
- centimetre (cm) — the width of your fingernail.
- metre (m) — about the width of a door.
- kilometre (km) — a long walk; about a 12-minute walk.
The whole family is held together by three simple facts. Figure 5.2 below shows them as a “ladder”.
So the three conversions to remember are:
1 cm = 10 mm
1 m = 100 cm
1 km = 1000 m
How do you actually convert? Just one rule:
- Going to a smaller unit (like m to cm), you multiply. (Smaller units are tinier, so you need more of them.)
- Going to a bigger unit (like cm to m), you divide. (Bigger units are larger, so you need fewer of them.)
Let us try a real conversion together.
A piece of cloth is 4 m long. How many centimetres is that?
- We are going from metres (bigger) to centimetres (smaller). Going to a smaller unit means we multiply.
- The fact we need is 1 m = 100 cm.
- So we multiply the number of metres by 100: 4 × 100.
- 4 × 100 = 400 cm. So 4 m = 400 cm.
Notice one small but important habit: always write the unit. “4” alone means nothing. “4 m” tells the full story.
Measuring length correctly
Having a scale is not enough. You must use it the right way, or your answer will be wrong even with a perfect scale. There are three things to get right.
1. Place the scale correctly. Keep the scale touching the object, lined up straight along its length. Do not leave a gap between the object and the scale.
2. Keep your eye directly above the point you are reading. This one surprises many students, so let us slow down and see why it matters.
When you look at the end of the object on the scale, your eye must be straight above that point. If you look from the left or the right, the end seems to line up with a different mark. The object did not change — but your wrong eye angle gives a wrong reading. This mistake, caused by looking from the wrong angle, is called a parallax error. Figure 5.3 below shows the three positions.
3. Handle a broken or worn scale. Many school scales have a worn-out or broken zero end. Do not throw them away. Just start from any clear full mark instead of zero — say the 1.0 cm mark. Then read the other end, and subtract. Figure 5.4 below shows how.
There is one more case. What if the line is curved, like a winding path on a map or a string of decoration lights? A straight scale cannot bend along a curve.
The trick is to use a piece of thread. Lay the thread along the curve so it follows every bend. Mark where it starts and ends. Then pull the thread straight and measure it on a scale. Figure 5.5 below shows both steps. (A flexible measuring tape, like a tailor’s tape, can also be used the same way.)
Let us refresh one bit of earlier maths that we just used in the broken-scale trick.
Motion and rest
Now we move from “how long” to “is it moving”.
To talk about motion, we first need a reference point. A reference point is a fixed object or place that we measure positions from. For example, a road sign “Delhi 70 km” uses Delhi as the reference point — it tells you your position is 70 km from Delhi.
Why do we need a fixed reference point? Because “near” and “far” make no sense on their own. Near what? Far from what? Once we fix a point to measure from, everyone agrees on the position.
Now the key idea:
An object is in motion if its position keeps changing with time (with respect to a reference point). An object is at rest if its position does not change with time.
That is it. Motion is just change of position over time.
Here is something that feels strange but is true: whether a thing is moving can depend on the reference point you choose.
Picture yourself sitting in a moving bus. Compared to the seat next to you, you are at rest — you are not sliding around. But compared to a tree outside, you are moving fast. Same person, same moment. The answer changes because the reference point changed. This is why we must always say what we are measuring from.
A girl sits still in a moving train. Is she at rest or in motion?
Both answers can be correct — it depends on the reference point. Compared to her seat (inside the train), she is at rest. Compared to a platform or a tree outside, she is in motion. Motion is always measured with respect to a reference point.
Types of motion — linear, circular, and oscillatory
Things do not all move in the same way. Watch the world and you will see a few clear patterns. There are three main kinds to know.
1. Linear motion (also called rectilinear motion). This is motion along a straight line. The word “rectilinear” simply means “straight-line”. An orange dropping straight down from a tree, or a car going straight down an open road, shows linear motion.
2. Circular motion. This is motion along a circular path — round and round. A merry-go-round in a park, or a stone tied to a thread and whirled around, shows circular motion.
3. Oscillatory motion. This is motion to and fro about a fixed position — back, then forth, then back again. A swing, or a pendulum in a clock, shows oscillatory motion.
Figure 5.6 below shows all three side by side.
Now, what about the word periodic? A motion is periodic if it repeats itself after a fixed time, again and again. A circle keeps going round — that repeats. A swing keeps going to and fro — that repeats too. So both circular and oscillatory motion are periodic. Linear motion in a straight line, by itself, does not repeat, so it is not periodic.
Let us put the three types side by side so the differences are clear.
| Type of motion | Path it follows | Everyday example | Does it repeat? |
|---|---|---|---|
| Linear (rectilinear) | A straight line | A car on a straight road; a falling orange | No |
| Circular | A circle (round and round) | A merry-go-round; a whirled stone | Yes — it is periodic |
| Oscillatory | To and fro about a fixed point | A swing; a clock's pendulum | Yes — it is periodic |
Why is the motion of a swing called periodic, but a car driving straight to the next town is not?
A swing repeats the same to-and-fro path again and again after a fixed time, so it is periodic. A car driving straight does not come back and repeat the same path — it just keeps going forward — so its straight-line motion is not periodic.
Common Mistakes
A measurement is just a number, so '5' is a complete length.
In everyday talk we often drop the unit and just say a number — 'I'm 5 tall', 'give me 2'. So it feels like the number alone is the answer.
A length always needs two parts: a number and a unit. '5' could be 5 cm, 5 m, or 5 km — wildly different sizes. Always write the unit, like 5 cm, with a space before it.
To measure with a scale, line up the very end (edge) of the scale with the object.
The physical edge of the ruler looks like the natural starting point, and on a brand-new ruler the zero mark really is near the edge — so it seems safe to start from the edge.
Start from a clear marking, normally the zero mark, not the physical edge. The edge is often worn or broken and does not sit exactly at zero. If zero is unclear, start from any full mark and subtract.
It does not matter where your eye is when you read the scale — the mark is the mark.
The marks are printed right there and look fixed, so it seems like you should read the same value from any angle.
Eye position changes the reading. From an angle, the end of the object seems to line up with a different mark. Your eye must be straight above the point you are reading to get the true value.
A person sitting in a moving bus is simply 'at rest' because they are sitting still.
The person isn't wriggling or walking, so 'sitting still' feels exactly the same as 'at rest'.
Whether they are at rest or in motion depends on the reference point. Compared to the bus seat they are at rest, but compared to a tree outside they are moving. Motion is always with respect to a reference point.
Quick Check
Five friends measure the same table with their own handspans and get different answers. What is the main reason?
Which of these is correct?
A clock's pendulum swings to and fro again and again. What type of motion is this?
The zero end of your scale is worn out. You place the object from the 2.0 cm mark and its other end is at the 11.0 cm mark. What is its length?
Practice Problems
Easy
Convert 7 m into centimetres.
Step 1: We go from metres (bigger) to centimetres (smaller), so we multiply.
Step 2: Use 1 m = 100 cm.
Step 3: 7 × 100 = 700 cm. So 7 m = 700 cm.
Convert 3 cm into millimetres.
Step 1: We go from cm (bigger) to mm (smaller), so we multiply.
Step 2: Use 1 cm = 10 mm.
Step 3: 3 × 10 = 30 mm. So 3 cm = 30 mm.
Name the type of motion: a child going round and round on a merry-go-round.
The merry-go-round moves along a circular path (round and round). So this is circular motion. It also repeats, so it is periodic too.
Medium
Convert 5 km into metres, and then 2 m into millimetres.
Part 1 — 5 km to m: Going from km (bigger) to m (smaller), we multiply. Use 1 km = 1000 m. So 5 × 1000 = 5000 m.
Part 2 — 2 m to mm: First 2 m = 2 × 100 = 200 cm. Then 200 cm = 200 × 10 = 2000 mm. So 2 m = 2000 mm.
A pencil is placed on a scale with a broken zero end. One end is at the 1.5 cm mark, the other end is at the 13.0 cm mark. What is the length of the pencil?
Step 1: With a broken end, the length is the bigger reading minus the smaller reading.
Step 2: Length = 13.0 cm − 1.5 cm.
Step 3: 13.0 − 1.5 = 11.5 cm. The pencil is 11.5 cm long.
A boy is cycling on a straight road. His friend says the boy is at rest because the boy is sitting on the cycle seat without moving his body. Is the friend right? Explain.
The friend is only partly right, and it depends on the reference point.
Compared to the cycle seat, the boy is at rest — he is not sliding around on the seat. But compared to a tree on the roadside, his position keeps changing with time, so he is in motion.
Since the question is about a boy “cycling on a road”, the natural reference point is the road, and with respect to the road he is clearly in motion. So the friend’s reasoning is wrong — sitting still on the seat does not make him at rest with respect to the road.
Challenge
You need to find the length of a curved wire that bends like the letter S. You only have a straight 15 cm scale and a piece of thread. Describe exactly how you would measure it, and if the straightened thread reads 1.0 cm at one end and 23.5 cm at the other, what is the length of the wire?
How to measure: A straight scale cannot bend along the S-curve, so use the thread. Lay the thread carefully along the wire so it follows every bend exactly. Mark or hold the two points where the wire starts and ends. Then take the thread off, pull it straight, and lay it along the scale. Read both ends.
Now the number: The thread is laid from 1.0 cm to 23.5 cm on the scale. The length is the bigger reading minus the smaller reading.
Length = 23.5 cm − 1.0 cm = 22.5 cm.
So the curved wire is 22.5 cm long, even though it is longer than the 15 cm scale — the thread let us measure something the scale could not reach in one go.
Sort these into linear, circular, or oscillatory motion: (a) a stone dropped straight down from a roof, (b) the hands of a wall clock going around, (c) a child on a swing, (d) a train moving straight on a straight track.
(a) A stone dropped straight down moves along a straight line → linear (rectilinear) motion.
(b) The clock hands go round and round along a circle → circular motion (also periodic, since it repeats).
(c) A swing moves to and fro about a fixed point → oscillatory motion (also periodic).
(d) A train on a straight track moves along a straight line → linear (rectilinear) motion.
Summary
- To measure length is to compare it with a fixed amount called a unit. Every measurement has two parts: a number and a unit (like 5 cm).
- Body-part units (handspan, foot, finger-width) fail because they differ from person to person, so the same object gives different answers. This is why we use standard units.
- The standard (SI) unit of length is the metre (m). The key conversions are: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m. Going to a smaller unit you multiply; to a bigger unit you divide.
- To measure correctly: place the scale touching the object, keep your eye straight above the reading point, and for a broken end start from a clear mark and subtract.
- A curved line is measured with a thread: lay it along the curve, then straighten it and measure it on a scale.
- A reference point is a fixed point we measure positions from. An object is in motion if its position changes with time, and at rest if it does not — always with respect to a reference point.
- Main types of motion: linear/rectilinear (straight line), circular (round and round), and oscillatory (to and fro). Circular and oscillatory motion repeat, so they are also periodic.
What’s Next
You now know how to measure how long things are and how to describe the way they move. Next, in Chapter 6 — Materials Around Us, you will look closely at the stuff things are made of. Why is a spoon made of metal but a cup sometimes made of glass? What makes some materials hard, some soft, some shiny, some see-through? You will start sorting the materials around you by their properties — and measurement will keep helping you compare them.
Frequently Asked Questions
Why do we use standard units of measurement instead of hand or foot?
Long ago people used body parts like hand-spans and foot lengths to measure, but every person's hand is a different size, so the same object gave different measurements to different people. This caused confusion in trade, building and science. Standard units like the metre are fixed the same everywhere in the world, so everyone gets the same answer when they measure the same thing.
How do you convert centimetres to metres and metres to kilometres?
There are 100 centimetres in 1 metre, so divide by 100 to convert cm to m (e.g. 250 cm = 2.5 m). There are 1000 metres in 1 kilometre, so divide by 1000 to convert m to km (e.g. 3500 m = 3.5 km). To go the other way, multiply — 4 m = 400 cm and 2 km = 2000 m.
What is the correct way to measure length with a ruler or scale?
Do not start from the 0 end of the scale if it is broken or worn — start from any clear marking and subtract. Place the scale flat along the object with the markings touching it. Keep your eye directly above the reading point, not to the side, so you avoid a parallax error. For a curved length like a piece of string, lay a thread along the curve, mark the ends, then measure the straight thread.
What is the difference between linear motion circular motion and oscillatory motion?
Linear motion is movement in a straight line, like a car on a straight road or a ball thrown forward. Circular motion is movement along a circle, like the blades of a fan or the Earth going around the Sun. Oscillatory motion is a back-and-forth or to-and-fro movement, like a swing or a pendulum clock. Some objects show more than one type at the same time.
What does rest and motion mean in science class 6?
An object is said to be at rest when its position does not change compared to something fixed around it — a book lying on a table is at rest. An object is in motion when its position keeps changing — a moving bus is in motion. Importantly, rest and motion are always relative to a fixed point of reference.