Class 6 Science Chapter 5: Measurement of Length and Motion

A New Uniform in Haryana

Deepa is eleven and lives in a town in Haryana. The school year has started and she has grown taller, so she needs a new uniform. At the cloth shop her mother asks for a two-metre piece and the shopkeeper measures it out with a metal measuring rod.

Three Instruments in One Afternoon

Then the tailor takes her measurements with a flexible measuring tape. Her mother tells him to make the uniform longer by char angula, meaning four finger widths. So in one afternoon Deepa has met a rod, a tape and a hand, and all three were measuring.

What the Friends Remembered

She tells her friends and they start swapping examples. Hardeep has seen his grandmother measure cloth by the length of her arm. Padma has watched a farmer divide a field into beds by walking and counting his strides. Anish adds that people sometimes use the length of their feet.

Let Us Try It Ourselves

So they decide to measure something. Tasneem suggests the classroom table. Padma asks which body part to use, and Deepa proposes the handspan, which her mother calls balisht. Hardeep sensibly suggests they all write their measurements down.

Five Answers to One Question

The results do not agree. Padma makes it 13 handspans and Hardeep makes it 14. Anish gets slightly more than 13, Tasneem slightly less than 13, and Deepa somewhere between 13 and 14. One table, five numbers.

Whose Measurement Is Wrong?

None of them. Padma puts the first question: what, then, is this table actually as long as? Hardeep puts the better one: why should the number come out different at all? Tasneem guesses the answer.

Checking the Guess

Her guess is that their handspans are different sizes. Anish says the obvious thing: let us check. So all five put their handspans side by side, and they are indeed different. The guess is confirmed rather than assumed, which is how it should be done.

Two Parts to Every Answer

Look at what they actually wrote. The length of the table was expressed in terms of handspans, and each answer has two parts. If the table is 13 handspans long, then 13 is the number and handspan is the unit chosen for the measurement.

The Unit Is Part of the Answer

That matters more than it sounds. Thirteen on its own means nothing at all. Thirteen handspans means something. A measurement is a number and a unit together, and leaving the unit off does not shorten the answer, it destroys it.

Why This Cannot Go On

Handspans and similar units, such as the length of a hand, a foot, a fist or the fingers, differ from person to person. So two people measuring the same thing honestly and carefully will still disagree. Something is needed for which that does not happen.

What Deepa Concluded

She says it thoughtfully: small wonder that people reach for a scale or a measuring tape. That is exactly the point of the whole activity. The problem was not that anybody measured badly. The problem was the unit.

India Measured Long Ago

This is not a new problem and India has a long history with it. Angula, which is a finger width, and its multiples, the dhanusa and the yojana are among the units named in ancient Indian literature. They were used for measuring artefacts, architecture and town planning.

Still in Use

The angula has not disappeared. Carpenters and tailors of the old school measure with it to this day. That is why Deepa's mother could say char angula to a tailor and be understood at once.

Dug Out of the Ground

There is older evidence still. Diggings at Harappan Civilisation sites have brought up a number of pieces ruled with regular markings, and several of them look very like scales. People there were marking out measured lengths a very long time ago.

The Question That Follows

So everybody agrees a shared unit is needed. Which one, and who decides? That turns out to have taken several countries and a long argument, and it is the next topic.

Scenario:

A class measures the same desk using handspans. Eleven children report eleven numbers, from six spans to nine. Rohit says somebody must have counted wrongly. The class checks by measuring one child's span against another's and finds the spans themselves differ by several centimetres. Nothing was counted wrongly at all. Their teacher asks what would happen if a carpenter took an order in handspans. The class works it out: the carpenter's span and the customer's span are not the same, so the furniture would come back the wrong size. Meera writes the conclusion. A measure that travels between people has to be the same for everybody.

Analysis:

Eleven honest measurements disagreed because the unit moved. The fault was in the ruler, not in the counting.

Activity:

Measure your classroom's width in handspans, then in feet placed heel to toe. Compare with three classmates and explain the spread.

Title:

The family handspan survey

Safety:

Measure something at floor or table height. Do not climb on furniture, and do not reach across anything hot, sharp or breakable.

What You Notice:

The person with the smallest hand gets the largest number, and the two rankings run in opposite order. That is the whole idea in one table: the object never changed, so every difference came from the unit.

Diggings at Harappan Civilisation sites have turned up pieces ruled with regular markings, and some may have been scales.

Carpenters and tailors who follow the old practice still measure in angulas today.

Char angula means four finger widths, and Deepa's mother used it to tell the tailor how much longer to make her uniform.

What a measurement is made of — A number and a unit, always both — Thirteen alone means nothing. Thirteen handspans means something.

Ancient Indian units — Angula, dhanusa, yojana — Smallest to largest. The first is a finger width and is still in use.

Everyone Solved It Their Own Way

The last topic ended with a clear need: a unit that does not change with the person using it. People did work that out, and several systems of units grew up in different parts of the world. Each one worked perfectly well at home.

Then People Started Travelling

The trouble began when people moved from one place to another and took their units with them. It created a lot of confusion, because agreement inside a region is no use at all once you cross out of it. A local answer to a shared problem is only half an answer.

One Agreement Instead

So several countries sat down together and settled on one agreed family of units for measuring. What everybody works with today goes by the name International System of Units, shortened in practice to SI units.

The Unit of Length

Within that system, length is measured in metres. The SI unit of length is the metre, and its symbol is m. Everything else about measuring length is built on that one choice.

Opening Up a Metre Scale

Take a metre scale and look at how it is divided. One metre is divided into 100 equal divisions, and each division is called a centimetre. So a centimetre is not an arbitrary length. It is a hundredth of a metre, by construction.

The Scale in Your Geometry Box

You are more likely to be carrying a smaller piece of the same idea, a scale about 15 cm long. Look at it carefully. Numbered marks run from 0 to 15 along it, and one centimetre is the distance from any big mark to the next — from 1 to 2, for instance.

Looking Closer Still

Now look between two of those big marks. Every centimetre has been cut again into ten equal slices, and a slice of that size carries the name millimetre. So a millimetre is a tenth of a centimetre, and 1 mm = 0.1 cm.

The Smallest You Can Read

That also tells you the limit of the instrument. On this scale, a millimetre is the finest length you can read off. Anything smaller lies beyond what these markings can tell you, however carefully you look.

And for Longer Distances

A metre is a sensible size for a room, but not for a road. Longer distances call for a bigger unit, and that is the kilometre, worth 1000 metres. Shorter ones send you the other way, to centimetres or millimetres.

The Three Conversions

Three lines cover everything you need. One kilometre is 1000 metres. One metre is 100 centimetres. One centimetre is 10 millimetres. Learn those three and any conversion in this chapter follows from them.

Choosing Well

So ask yourself: would it be convenient to state in metres how far the railway runs from one city to the next? Or to give one page of a book its thickness that way? Both are possible and both are silly. Pick the unit that keeps the number manageable.

The Other Scale Markings

Some scales carry a second row of numbers. These are inches, and one inch works out at 2.54 cm. The inch and the foot were the everyday units of length in earlier days, and some people have never given them up.

How to Write a Unit

There are rules, and they are worth getting right. Write kilometre, metre, centimetre and millimetre in small letters, unless one of them happens to open a sentence. The symbols km, m, cm and mm take small letters as well.

Three More Rules

Never add an s to a symbol for the plural, so five centimetres is 5 cm and not 5 cms. Keep full stops off a symbol too, unless the sentence happens to finish there. And put a space in front of the unit: 5 cm, not 5cm.

And Never Drop the Unit

One last reminder from the previous topic. When a length goes down on paper, the unit has to go down with it. Your result comes in two pieces: the number, and the unit it was measured in.

Scenario:

A class reads that different parts of the world once used different systems of measurement. Sana asks why anybody bothered to change. Their teacher asks the class to imagine ordering cloth from another country under the old arrangement. Every quantity would have to be converted, and a mistake in the conversion would spoil the order. The class then considers what agreement cost. Each country gave up a system it was used to. Nobody was forced, and the gain was that a number now means the same thing in every country that joined. Sana sees that the International System of Units is an agreement between people rather than a discovery about the world.

Analysis:

Standard units were not found, they were agreed. Each country gave up something familiar and gained a number that travels.

Activity:

Find two older units still used near you, such as a bigha or a tola. Write what each measures and whether its size is the same everywhere.

Title:

Three units, one object

Safety:

Use a scale with rounded ends if you have one, and keep the edge away from your eyes. Do not measure anything hot, sharp or fragile.

What You Notice:

The three columns hold the same length written three ways, and only one of them reads naturally. An eraser in metres is 0.04 m, which is correct and useless. The circled column moves as the objects get bigger.

Several systems of units evolved in different parts of the world, and travel between them caused a great deal of confusion.

On a 15 cm scale, 1 mm is the smallest length you can measure.

Some scales carry a second set of markings in inches, where 1 inch is 2.54 cm.

The conversion ladder — km 1000, m 100, cm 10 — A kilometre holds 1000 metres, a metre 100 centimetres, a centimetre 10 millimetres.

Writing a unit — Small letters, no s, no full stop, one space — Four rules. 5 cm, never 5cm, never 5 cms, and never 5 cm. at mid-sentence.

A Right Unit and a Wrong Answer

You now know what a centimetre is and how to write it. That still does not guarantee a correct measurement. Two pupils can measure the same pencil with the same scale and disagree, and neither of them has broken a rule of units. The disagreement comes from how they used the instrument.

Lay It Along the Object

Start with the obvious. The scale has to be placed along the length you want, and it has to touch the object. A scale held a little above the pencil, or set at a slight angle across it, is measuring some other line through the air.

Zero at One End

Next, line up the zero mark of the scale with one end of the object. Then look at where the other end falls. If the object ends on the mark labelled 7, the object is 7 cm long, and you write it as 7 cm.

When the Zero End Is Worn

Scales live in pencil boxes and their ends take a beating. The first centimetre often goes worn, chipped or broken, and then the zero mark cannot be trusted. This does not mean you need a new scale.

Start From Any Full Mark

Instead of the zero, line up any other full mark with one end of the object. The mark labelled 2 will do. Now read where the far end falls, and suppose it falls on 9. The object did not start at zero, so the answer is not 9 cm.

Then Subtract

The length is the final reading minus the starting reading. Here that is nine take away two, which gives 7 cm. The rule is worth stating once and keeping: length equals the reading at the far end minus the reading at the near end.

Where Your Eye Sits

Now for the part that catches almost everybody. Having placed the scale perfectly, you still have to look at it, and the direction you look from changes what you see. Your eye must be directly above the mark you are reading.

Looking From a Slant

If you tilt your head to the left, the mark appears to shift to the left. Tilt to the right and it appears to shift the other way. The object has not moved and the scale has not moved. Only your line of sight has, and that is enough to give a wrong reading.

Try It and Watch It Happen

This is easy to see for yourself. Put a pencil against a scale, keep your head still, and note the reading. Now lean well to one side without moving anything else, and read it again. The two numbers will differ, and you can watch the error appear.

So Keep Looking Straight Down

The cure is simple and needs no equipment. Position your eye vertically above the point you are reading, and read only that point. Then move your eye and repeat for the other end. Two readings, each taken from directly overhead.

The Problem With a Curve

A straight scale is a straight edge, so it can only lie along a straight line. Ask it for the length of a curved line on a page, or the curve of a bangle, and it simply cannot follow the shape. A different idea is needed.

A Thread Will Follow Anything

Take a thread and lay it carefully along the curved line, pressing it down so it follows every bend without stretching and without cutting corners. Mark the thread at the point where the line begins and again where it ends.

Straighten It Out

Now lift the thread off, hold it straight along your scale, and read the distance between your two marks. That distance is the length of the curved line. You have turned a shape the scale could not handle into a straight length it can.

Why It Works

The thread is the trick, and the reason is that it does not stretch. It is the same piece of thread whether it is curled along the curve or pulled out straight, so its length has not changed. Only its shape has.

The Four Habits

Put together, correct measurement is four habits. Lay the scale along the object and touching it. Set a clear mark at one end. Read each end from directly above. Subtract if you did not start at zero. And, as always, write the unit.

Scenario:

A class measures a pencil and gets two answers. Imran reads fourteen centimetres and Nita reads thirteen. Both used the same scale and the same pencil. Their teacher asks each to show how they held it. Imran lined the pencil up with the worn end of the scale, where the zero mark has rubbed away. Nita started at the one centimetre mark and subtracted. The class works out that Imran's reading carries whatever the worn end has lost. They agree a rule for the whole class. Start from a mark you can actually see, note where you started, and subtract it at the end.

Analysis:

The scale was the same and the starting point was not. A worn zero adds its own error to every reading taken from it.

Activity:

Measure the same object three times, starting at 0, at 2 and at 5 centimetres. Subtract correctly each time and check the three answers agree.

Title:

Make the error happen on purpose

Safety:

Keep the scale edge away from your face while you lean. Do not press a thread hard around a finger, and use a plastic bangle rather than a glass one.

What You Notice:

The three readings of the same pencil differ, and the difference grows the further you lean. The subtraction from the 2 mark returns the original length exactly. The thread gives the bangle a length that no straight scale could have reached.

A scale with a worn zero end still measures perfectly well, as long as you subtract your starting reading.

Looking at a scale from one side makes the mark appear to shift, which is why two pupils can read the same object differently.

A thread can measure a length no straight scale can reach, such as the curve of a bangle.

Four checks before reading — Along, touching, zero, overhead — Scale along the object, touching it, zero at one end, eye directly overhead.

A worn zero end — Start anywhere, then subtract — Any full mark will do as a start, provided you take it off the final reading.

Two Hundred Metres From Where?

Suppose somebody tells you the shop is two hundred metres away and then walks off. You are no better informed than before. Two hundred metres measured from where? A length on its own does not place anything. It needs a starting point to be measured from.

Choosing a Reference Point

That starting point is called a reference point. The shop is two hundred metres from the bus stop, or from the school gate, or from the neem tree at the corner. Now the sentence works. The position of an object is always described with respect to some reference point.

You Do This Already

You use reference points without thinking about them. Your desk is the third from the door. The switch is beside the window. The temple is just past the bridge. In each case something fixed has been named, and the position follows from it.

Now Add Time

Fix a reference point and note where an object is. Leave it a while, then look again. If it is in the same place, nothing has happened. If it is somewhere else, the object has moved. That comparison over time is the whole idea of motion.

Rest

An object whose position does not change with time is said to be at rest. The blackboard is at rest with respect to the wall. So is your bag on the floor, and so is the tree in the playground, for as long as you care to watch it.

Motion

If the position of an object changes as time passes, the object is in motion. A cyclist passing the gate, a ball rolling across the floor, the hand of a clock, a bird crossing the sky. Each one is somewhere different when you look again.

The Same Object, Two Answers

Here is where it gets interesting. Sit in a moving bus and ask whether you are moving. With respect to the seat beside you, no. It is exactly where it was and stays there. With respect to a tree outside, yes, and quite fast.

Both Answers Are Right

Neither answer is a mistake. They use different reference points, and rest and motion are always stated with respect to something. This is why a careful answer names the reference point rather than leaving it to be guessed.

Sorting Motion by Its Path

Not all motion looks alike. Watch a train, a fan and a swing for a minute each and you have watched three different kinds of movement. What separates them is the shape of the path the object follows.

Motion Along a Straight Line

A train on a straight track, a ball rolling down a straight slope, a lift going up its shaft, a march past along a road. The path is a straight line, and this is called rectilinear motion. It is also described as linear motion.

Motion Along a Circle

The blades of a ceiling fan, a merry-go-round, the hands of a clock, a stone whirled on a string. Each one turns about a fixed centre and traces a circular path. This is circular motion.

Motion To and Fro

A child on a swing, the pendulum of a wall clock, the needle of a sewing machine, a ruler twanged at the edge of a desk. Each goes one way, comes back, and does it again about the same fixed position. This is oscillatory motion.

Telling Them Apart

So you have a simple test with three answers. Follow the path with your eye. Straight line, rectilinear. Round a centre, circular. Backwards and forwards over the same stretch, oscillatory. The object itself does not tell you. The path does.

Two Kinds at Once

Real objects are not always so tidy. A wheel rolling along a road is turning about its centre and at the same time moving forward along the road. Both descriptions apply, and you name whichever part of the motion you are talking about.

And Back to Measuring

Motion and measurement belong together. Once an object has moved you can ask how far, and the answer is a length: the distance it has travelled. It is written the same way as any other length, a number with its unit.

Scenario:

Ishan leaves his bicycle outside the gate every evening and finds it there every morning. On Tuesday morning he is sure somebody has taken it out and brought it back, because it is not quite where he left it. His sister disagrees, and says he is only guessing. So on Wednesday evening Ishan decides to settle the matter properly. He chalks a line on the road, notes exactly how far the front wheel stands from the gatepost, and writes the figure in his notebook with the time beside it. On Thursday morning he measures again in the same way. The two figures differ by eleven centimetres. His sister now says this still proves nothing, because the postman leans bicycles aside every day.

Analysis:

Ishan has done the right thing: he fixed a reference point, recorded a position, and looked again after a stretch of time. What is in question is not his method but what a difference of eleven centimetres is allowed to mean.

Activity:

Choose something at home that you believe nobody touches, such as a chair or a flowerpot. Pick a fixed reference point near it, measure the distance to it, and write down the figure with the date and time. Repeat for five days without looking at your earlier entries first. Then compare all five and decide what your readings really show.

Title:

A motion survey of your own house

Safety:

Keep well clear of a working fan and of anybody on a swing. Do not put a hand near a sewing machine needle or any moving wheel.

What You Notice:

The three columns fill up unevenly, and oscillatory is usually the hardest to fill. The object that belongs in two columns is almost always something with a wheel. The last question is the one that needs most care, because the answer depends entirely on who is watching and from where.

A passenger asleep in a moving train is at rest with respect to her seat and in motion with respect to the platform.

The tip of a fan blade is in circular motion while the fan as a whole stays exactly where it is.

The needle of a sewing machine moves up and down about the same place, which makes it oscillatory.

The three types of motion — Straight, round, to and fro — Rectilinear along a line, circular about a centre, oscillatory back and forth.

Testing for motion — Position, plus time, plus a reference point — All three are needed. A changed position over time is motion, but only against something fixed.