Measurement of Length and Motion: Class 6 Science · Chapter 5

Why measure?

Your cousin in Guwahati calls you. “How big is your new kite?” she asks. You stretch out your arms and say, “This big!” But she cannot see your arms over the phone. So how can you tell her? You need to compare the kite with something you both know.

People measure things all day long. A tailor wraps a soft tape around a customer’s waist. A mason checks a wall with a long steel tape. A carpenter unfolds a wooden rule to fit a door frame. In Tamil Nadu, a flower seller measures a string of jasmine against her forearm. All of them are doing one job: comparing a length with a length they already know. That is what measurement (मापन) means. Some of their tools are shown in Fig. 5.1.

In this chapter you will learn to measure lengths the way scientists do. Then we turn to things that move. How do we say where something is? And how do we know whether it is moving at all?

5.1 How do we Measure?

Long before rulers, people used their own bodies to measure. A mason might check a wall in haath, the length from the elbow to the tip of the middle finger. Children marking a gully-cricket pitch count their footsteps. Many elders still measure with a बालिश्त (balisht). That is the stretch from the tip of the thumb to the tip of the little finger of an open hand. We call it a handspan.

Body measures are always with you, and they cost nothing. So what could go wrong? Look at Fig. 5.2.

Riya’s answer is “12 handspans” and Dadaji’s is “8 handspans”. Neither of them is wrong! Each answer has two parts: a number (12 or 8) and a unit (मात्रक), which here is the handspan. The trouble is that Riya’s unit and Dadaji’s unit are not the same size. A bigger unit fits fewer times, so it gives a smaller number.

Now imagine buying 20 handspans of ribbon, first from a shopkeeper with small hands and then from one with big hands. You would get different amounts of ribbon for the same money! For fair buying and selling, and for careful work, we need a unit that is the same for everyone, everywhere.

5.2 Standard Units

Imagine a silk seller in Surat and a buyer from faraway Kolkata. The seller’s haath may be longer or shorter than the buyer’s. So how much silk is “20 haath”, really? Arguments like this once happened all over the world, because every place had units of its own. Today almost every country uses one agreed set of units, the International System of Units. We call them SI units for short.

A standard unit (मानक मात्रक) means exactly the same amount to everyone, in every country. For length, the SI unit is the metre, written m for short. A metre is roughly the height of a door handle above the floor.

Nobody measures an eraser in metres: the number would be tiny and awkward. Small things need a smaller unit, and 100 centimetres (cm) make one metre. On the scale in your geometry box, the numbered marks are 1 cm apart. Now zoom in with Fig. 5.3.

What about the tiny lines between the numbers? Choose any centimetre on your scale and count the small gaps inside it. You will find ten, all equal. Each gap is one millimetre (mm). So 10 mm make 1 cm, and $1\mathrm{m}\mathrm{m}=0.1\mathrm{c}\mathrm{m}$. The scale has nothing finer than these gaps, so 1 mm is the smallest length you can read on it.

For long distances, even a metre is tiny. Nobody says their grandparents’ village is 12,000 metres away. We say it is 12 kilometres (km) away. One kilometre is 1000 metres.

The staircase in Fig. 5.4 helps you convert. When you step down to a smaller unit, more of the small units fit, so the number gets bigger: you multiply. When you step up to a bigger unit, you divide.

5.3 Correct Way of Measuring Length

Would you measure a matchbox with a long steel tape? Or a whole room with a 15-cm scale? Each job has a tool that suits it best. Short, straight things suit a small scale. Long, straight things suit a metre scale or a steel tape. Round things need something soft that bends. The table sorts out a few tools and jobs.

Then follow three simple rules.

Lay the scale along the object

The marked edge of the scale should touch the object all the way along, with no gap and no tilt. A tilted scale leaves a gap, and the reading goes wrong. Watch out for the ends too. On many scales the zero is a little way in from the edge, so start from the zero mark, not from the end of the plastic.

Keep your eye straight above the mark

A scale has some thickness. So when you look at the end of an object from one side, it seems to line up with the wrong mark. From one side the reading comes out too small, and from the other side too big. Always bring your eye straight above the point you are reading, as in Fig. 5.6.

What if the scale is broken?

Snap! Your scale has lost its first two centimetres. Do you need a new one? Not at all. Think of a length as the gap between two readings. When one end of an object sits on 0, the far reading equals the gap, so you read the length straight off. When one end sits on 2 cm, the gap is the far reading take away 2. So line the object up with any mark you can read clearly, and subtract, as in Fig. 5.7.

5.4 Measuring the Length of a Curved Line

Why do tailors use a soft tape and not a stiff scale? Because many things we want to measure are not straight. Think of the curved border of a rangoli, the rim of a bangle, or a river winding across a map. A stiff scale cannot bend to follow a curve.

A soft tape measure can follow a curve by itself. No soft tape at home? A plain thread works just as well, as Fig. 5.9 shows. Press the thread along the curve bit by bit, and mark it where the curve starts and ends. Once it is pulled straight, a scale can measure the gap between the two marks.

A wheel’s rim is a curve too, and it gives us a neat trick for measuring long distances. Each time a wheel turns once, it rolls forward by exactly the length of its rim, as Fig. 5.10 shows.

5.5 Describing Position

You are looking for the library. The man at the tea stall points and says, “Just 300 m that way.” Further back, a bus conductor at the bus stop says, “It is 800 m down this road.”

The two numbers do not match, yet neither man is wrong. A distance always has two ends, and each man put one end where he was standing. The tea stall is simply nearer to the library than the bus stop is. See it in Fig. 5.11.

To describe a position so that nobody gets confused, we first choose one fixed place. Then we give every distance (दूरी) from that place. That agreed fixed place is our reference point (संदर्भ बिंदु). In Fig. 5.11, the temple gate makes a good reference point. Everyone knows it, and it never moves.

On highways you meet another kind of reference point. Small stones by the roadside, called milestones or kilometre stones, show the name of a town and a number. A stone saying “Mysuru 48” means that Mysuru is 48 km away. The town is the reference point, and the stone tells you your position from it (Fig. 5.12).

5.6 Moving Things

Look out of a window for a minute. Some things are moving: a bird, a bicycle, leaves in the wind. Other things stay still: a wall, a parked scooter, a lamp post. How do you decide which is which?

Scientists use the same test. Pick a reference point and watch for a while. Does the thing’s position, compared with that point, keep changing? Then the thing is in motion (गति). Does its position stay the same? Then it is at rest (विरामावस्था). Try the test on Fig. 5.13, two photos of a street taken five seconds apart.

Now for a puzzle. You sit in a train that is slowly leaving a station. Your friend Arjun sits two seats away. Is Arjun moving? Try the interactive below before you answer.

Arjun’s distance from you stays 2 m the whole time. So, with you as the reference point, Arjun is at rest. But his distance from the tea seller keeps changing. So, with the platform as the reference point, Arjun is in motion. Both statements are true at the same moment! Whether something is moving depends on the reference point you choose.

5.7 Types of Motion

A mango falling, a ceiling fan turning, a swing going back and forth: all three are moving, but in very different ways. Scientists sort motion by the shape of the path that an object follows. Let us look at three kinds.

Moving along a straight line

A straight-line path gives the simplest kind of motion, called linear motion (रैखिक गति). A bucket pulled up from a well, a ball rolling down a straight plank and a bus on a straight road all show it (Fig. 5.15). The line can point up, down, sideways or on a slant.

Moving along a circle

Some things never get anywhere, yet never stop moving. Think of a merry-go-round at a mela, or the blades of a ceiling fan: they just go round and round.

Going round and round along a circle is called circular motion (वृत्तीय गति). The tip of a fan blade, a cabin on a giant wheel, a mark on a potter’s wheel and the tip of a clock’s hand all move in circles (Fig. 5.16).

Moving to and fro

Now think of a swing. It moves forward, comes back, and moves forward again, over and over. Its path is neither a full circle nor a long straight line.

Moving back and forth, again and again, on both sides of a middle position, is called oscillatory motion (दोलन गति). For a swing or a hanging key, the middle position is where it hangs still when it is left alone. A swing, the pendulum of a wall clock, a see-saw and a plucked guitar string all oscillate.

Tick, tock, tick, tock. A pendulum clock keeps time because its pendulum takes the same time for every swing. Motion that repeats itself after equal gaps of time is called periodic motion (आवर्ती गति). A fan running at a steady speed and a swing pushed gently are periodic too. So circular and oscillatory motions are often periodic. A falling mango is not: it drops once and stops.