Welcome dear students! Today we are going to learn about Measurement of Length and Motion from Class 6 Science.
Let us begin with a story. Deepa, a curious eleven year old girl, lives in a town in the state of Haryana. The new school year has started. Deepa needs a new uniform since she has grown taller. Her mother takes her to a cloth shop. She asks for a two metre cloth piece. The shopkeeper measures the cloth using a metal measuring rod. Then, the tailor takes her measurements using a flexible measuring tape. Her mother instructs the tailor to increase the length of her uniform by char angula, which means four fingers width. Are the tape and rod similar to the scale that the elder sister has in her geometry box? What did mother mean by char angula? Deepa shares her experience with her school friends Anish, Hardeep, Padma, and Tasneem, and this leads to a discussion amongst them.
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Hardeep says, I have seen my grandmother measuring cloth by the length of her arm. Have you ever seen how a farmer measures length to divide his field into beds? He walks and counts the number of his strides, says Padma. Oh, not just the length of the strides, sometimes they also use the length of their feet to measure, adds Anish. Deepa says excitedly, Measuring length using body parts must be so much fun! Let us also measure something using a body part. What should we measure? Okay, let us measure the length of the table in our classroom, says Tasneem. Padma adds, And which body part should we use to measure it? Deepa says, Let us use our handspan. I will show you how to use it. I have seen my mother using it. She calls it balisht. Hardeep adds, Okay. Let us also note down our measurements. In Figure five point one, we see a student using their handspan to measure the length of a table by placing one handspan after another along the edge.
Let us look at their results. Anish measured slightly more than thirteen handspans. Padma measured thirteen handspans. Tasneem measured slightly less than thirteen handspans. Deepa measured between thirteen and fourteen handspans. Hardeep measured fourteen handspans. Padma says, Oh, the number of handspans is different for all of us. So, what can we say about the length of the table? But why should the number be different? Hardeep asked thoughtfully. Tasneem says, I can guess. Our handspans are of different sizes. Anish gives an idea, Let us check this. So, all five of them put their handspans along each other and arrive at the conclusion that the lengths of their handspans are different. Deepa says thoughtfully, No wonder people use scales and measuring tapes.
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Deepa and her friends compare the length of the table with the length of their handspans. The length of the table is expressed in terms of their handspans. Here, the handspan used for measurement is an example of a unit. And the length is expressed in two parts, a number and a unit. For example, if the length of the table is found to be thirteen handspans, then thirteen is the number and handspan is the unit selected for the measurement. However, handspans and other similar units, such as length of hand, foot, fist or fingers, differ from person to person. Thus, there is a need for such a unit for which measurements of the same length made by different people do not differ.
Let me share a fascinating fact from our More to know section. India has a rich history of measurement systems dating back to ancient times. Angula, which means finger width, multiples of angula, dhanusa, and yojana are some of the units mentioned in ancient Indian literature, and used in measuring artefacts, architecture, and town planning. The angula is still used by traditional craftspeople like carpenters and tailors. Several objects with ruled markings which could be scales have been excavated from sites of the Harappan Civilisation.
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Several systems of units evolved with time in different parts of the world. However, when people started travelling from one place to another, it created a lot of confusion. This led to different countries coming together and adopting a set of standard units of measurement. The system of units now used is known as the International System of Units, or SI units. The SI unit of length is metre. Its symbol is m. A metre scale is shown in Figure five point two. One metre is divided into one hundred equal divisions. Each division is called a centimetre. You may be familiar with a smaller part of the metre scale, typically fifteen centimetres long, shown in Figure five point three. Look carefully at the fifteen centimetre scale. It has markings in centimetres from zero to fifteen. The length of any section between two consecutive big marks, such as between one and two or between five and six, is one centimetre. Observe that these sections of one centimetre length are further divided into ten equal parts. The length of one of these smaller parts is called a millimetre. One millimetre is the smallest value of length that you can measure using this scale. One millimetre is equal to one tenth of a centimetre, which means one millimetre equals zero point one centimetre.
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For measuring larger lengths, we use a larger unit called a kilometre which is equal to one thousand metres. And for measuring smaller lengths, we use units such as centimetre or millimetre. Would it be convenient to use the unit metre to measure larger lengths, such as the length of a railway track between two cities, or to measure smaller lengths, such as the thickness of a page of a book? Let us remember these exact conversions: one kilometre equals one thousand metres. One metre equals one hundred centimetres. One centimetre equals ten millimetres. In some scales, you might have noticed another scale marking. This scale marking is in inches, where one inch equals two point five four centimetres. In earlier days, units, such as inch and foot, were used to measure length. These units are still used by some people.
Here is an important note from the textbook. Units of length, such as kilometre, metre, centimetre and millimetre, begin with a lowercase letter, except at the beginning of a sentence. Their symbols km, m, cm and mm are also written in lowercase letters, and are never followed by s for the plural. Note that a full stop is not written after the symbol, except at the end of a sentence. While writing the length, always leave a space between the number and the unit.
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Suppose we all measure the length of the table again, but this time using a metre scale. Will our results still be different? No, but we should first learn the correct way of using a scale to measure length. For measuring any length, we need an appropriate scale. For example, if you want to measure the length of your pencil, you may use a fifteen centimetre scale. Similarly, if the height of a room is to be measured, you may need a metre scale or a measuring tape. You cannot directly measure the girth of a tree or the size of your chest using a metre scale. For such measurements, flexible measuring tape, such as a tailor's tape is more suitable. While measuring lengths, we need to take care of some points.
What is the correct way to place the scale? Place the scale in contact with the object along its length as shown in Figure five point four. In part a, the scale is placed correctly, touching the object directly. In part b, the scale is placed incorrectly, held away from the object. What is the correct position of the eye while reading the scale? For example, if you are trying to measure the length of a pencil by aligning it with a scale, the position of your eye should be directly above the tip of the pencil. Figure five point five shows three eye positions labeled A, B, and C. Position A is to the left, position C is to the right, and position B is directly above. The correct position of the eye is B.
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How to measure the length if the ends of the scale are broken? If the ends of the scale are broken or the zero marking is not clear, it can still be used for measurement. With such a scale, use any other full mark of the scale, say, one point zero centimetre. Figure five point six shows a broken scale where the object starts at the one point zero centimetre mark and ends at the ten point four centimetre mark. Then you must subtract the reading of this mark from the reading at the other end. For example, in Figure five point six, the reading at one end is one point zero centimetre and at the other end, it is ten point four centimetres. Therefore, the length of the object is ten point four centimetres minus one point zero centimetre, which equals nine point four centimetres.
How do visually challenged students measure lengths? They use scales with raised markings that can be felt by touching them.
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Activity five point one: Let us measure. Select some objects around you, such as a comb, a pen, a pencil, and an eraser to measure their lengths. Measure their lengths one by one using a metre scale and note down the measurements in a table with two columns: Object and Length of the object. Why are some length measuring devices made up of flexible materials? They are made flexible so they can wrap around curved surfaces like chests or tree trunks to measure girth accurately. While writing the length, do not forget to write the unit also. Thus, your result will consist of two parts, one part is a number and the other part is the unit of measurement. Some of your friends in the class would have measured the length of the same objects. Compare the lengths measured by you with that of your friends. Are the measured lengths the same or slightly different? If not the same, discuss the possible reasons for the differences. Differences may occur due to slight variations in how the scale is placed, parallax error from eye position, or using different scales.
Anish and his parents fixed electric string lights on the arches of the verandah of their house, as shown in Figure five point seven, for a celebration at home. The figure shows a house with decorative arches over the doorway, covered with glowing string lights. How would they have measured the required length of string lights? In the case of a curved line, measurements can be made with the help of a flexible measuring tape or by using a thread as shown in Figure five point eight. Figure five point eight shows a curved line drawn on paper. A thread is placed carefully along the curve, marked at the start and end points, and then straightened out to be measured against a straight scale. The thread can then be straightened and its length can be measured using a metre scale.
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One day the teacher informs her students that she has planned an educational visit to a nearby garden. She asks the students to reach there directly in the morning. Deepa and her friends start discussing whether the garden would be closer than their school or farther. Tasneem and Padma say that the garden would be closer, while Deepa and Anish feel that the school would be closer. Hardeep thinks that both would be almost at an equal distance. Figure five point nine shows a map with a bus stand, a school, a garden, and the houses of Deepa, Anish, Hardeep, Tasneem, and Padma located at different distances from these places. Who do you think is correct? All of them are correct. Then, why are their observations different? They are locating the distances of the school and garden from their houses. If, instead, each of them had thought of distances from a same object or point, say, the bus stand, then their observations would have been the same. When distance is stated with respect to a fixed object or point, then this point is called a reference point.
A few days later, Hardeep tells his friends excitedly, Let us all go to the playground. The sports teacher wants us to help her to draw lines with chuna powder, which is limestone powder, for making the Kabaddi court for the sports day. Padma says, We will need a longer measuring tape. Let us take it from the sports room. Figure five point ten shows a rolled up flexible measuring tape with markings. Deepa says, Let us first decide the point on the ground from which we will measure the distances to start drawing the lines. Let us call this our reference point. Figure five point eleven shows students on a playground using a measuring tape starting from a marked spot labeled Reference Point to draw straight lines for a court.
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After a few days, Padma was travelling by bus to visit her grandparents in Delhi. She was eager to reach Delhi and was reading the kilometre stones on the side of the road. On one of the kilometre stones, it was written Delhi seventy kilometres. Figure five point twelve shows a stone pillar on a roadside with the text Delhi seventy kilometres painted on it. Further on, the next kilometre stone read Delhi sixty kilometres. Each kilometre stone indicated that she was getting closer to her grandparents house. These kilometre stones indicated her distance from Delhi. So, Delhi is the reference point in this situation. What do such kilometre stones indicate? How could Padma conclude that she was getting closer to her destination? Figure five point thirteen shows a road with two stones. The first says Delhi seventy kilometres, and the second says Delhi sixty kilometres, with an arrow showing the bus moving towards Delhi. If the kilometre stone reads Delhi seventy kilometres, we can say that the position of Padma is seventy kilometres from Delhi. When the kilometre stone reads Delhi sixty kilometres, the position of Padma is sixty kilometres from Delhi. Does this mean that the position of Padma, with respect to the reference point, is changing with time? Yes. When does the position of an object change with respect to a reference point? Does it change when an object is moving? Yes, it changes when the object moves.
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Activity five point two: Let us explore. Look around and prepare a list of five objects that are in motion and five objects that are at rest. Record your observations in a table with four columns: Objects in motion, Justification, Objects at rest, Justification. For example, a cow grazing in the field is in motion because its position changes with time. A tree is at rest because its position does not change with time. Compare and analyse your justifications. How can one decide if an object is in motion or at rest? An object is said to be in motion if its position changes with respect to the reference point with time. If an object is not changing its position with respect to the reference point with time, it is said to be at rest.
Deepa looked around her in the bus and noticed that all the passengers were seated. She looked around again after a minute and found them still occupying their seats. She wondered, Are they moving? She concluded that the position of the passengers was not changing with time. Therefore, they were certainly at rest. However, when she looked outside, she felt they were in motion as their positions were changing with respect to things outside. The reference point is important in deciding whether an object is at rest or in motion. If Deepa considered herself or the bus as the reference point, then the passengers were at rest. However, if she considered any object outside the bus, say a building, as the reference point, then the passengers and the bus were in motion.
Here is something to think over. Suppose you are travelling on a ship which is moving at a constant speed along a straight line on a calm sea. Suppose there is no window on the ship. Is there any way that you can determine whether the ship is moving or is stationary? Without external reference points, it is impossible to tell if the ship is moving at constant speed in a straight line.
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Activity five point three: Let us explore. Take an eraser and drop it from a certain height. Observe its motion. Does it move along a straight line? Yes. When an orange drops from the tree, does it move in a straight line? Yes. Have you seen the Republic Day parade? Recall the march past of students during the parade. Do they move on a straight line path? Yes. When a heavy box is pushed, it may also move along a straight line. Figure five point fourteen shows a person pushing a heavy box across a floor, with a straight arrow indicating its path. When an object moves along a straight line, its motion is called linear motion. Identify such linear motion in your surroundings.
But do things always move along a straight line? You might have enjoyed playing on swings and merry go rounds. Are these types of motion also linear motion? No. Activity five point four: Let us investigate. Tie an eraser or a potato to one end of a thread. Hold the other end of the thread with your hand and whirl it. Figure five point fifteen shows a hand holding a thread with an eraser at the end, moving in a circular path. Observe its motion. Is the motion of the eraser the same as that of a merry go round? Yes. When an object moves along a circular path, its motion is called circular motion.
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Activity five point five: Let us investigate. Tie an eraser or a potato to one end of a thread. Hang the eraser by holding the other end of the thread. Figure five point sixteen shows a hand holding a thread with an eraser hanging down, swinging slightly to one side. Keep your hand steady. Using the other hand, take the eraser slightly to one side and then release. Does it start moving to and fro? Yes. Is its motion similar to the motion of a swing? Yes. When an object moves to and fro about some fixed position, its motion is called oscillatory motion.
Activity five point six: Let us investigate. Take a thin metal strip of about fifty centimetres long. Hold its one end pressed to a table. You may use a few books or a brick to hold it. Figure five point seventeen shows a metal strip clamped at one end by books on a table, with the free end vibrating up and down. Press the free end of the strip slightly and let it go. Observe the motion of this end of the strip. Does it move up and down? Yes. This is also an example of oscillatory motion.
If an object repeats its path after a fixed interval of time, its motion is said to be periodic. When an object is in circular motion, it moves along the circular path again and again. An object in oscillatory motion also repeats its motion while moving to and fro. Both circular and oscillatory motion are periodic in nature.
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Activity five point seven: Let us identify. Look at the picture of a children's park or visit a children's park. Figure five point eighteen shows a lively park with a slide, a swing, a merry go round, a seesaw, and children playing. Observe different kinds of motions. Classify them as linear, circular or oscillatory motion. List them in a table with columns for Object, Linear motion, Circular motion, and Oscillatory motion. Give your justification for why you put each in a certain category. For example, a swing moves to and fro, so it is oscillatory motion. A merry go round moves in a circle, so it is circular motion. A child sliding down a slide moves in a straight line, so it is linear motion.
Let us quickly review the keywords and summary. The International System of Units or SI units has been adopted by countries as standard units of measurement. The SI unit of length is metre. Its symbol is m. One kilometre equals one thousand metres, one metre equals one hundred centimetres, one centimetre equals ten millimetres. When distance is stated with respect to a fixed object or point, then this point is called a reference point. An object is said to be in motion if its position changes with respect to a reference point with time. When an object moves along a straight line, its motion is called linear motion. When an object moves along a circular path, its motion is called circular motion. When any object moves to and fro about any fixed position, its motion is called oscillatory motion.
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Now, let us enhance our learning by solving the exercises together. Question one asks us to match lengths with suitable units. Distance between Delhi and Lucknow matches with kilometre. Thickness of a coin matches with millimetre. Length of an eraser matches with centimetre. Length of school ground matches with metre.
Question two asks us to mark True or False. Statement one: The motion of a car moving on a straight road is an example of linear motion. This is True. Statement two: Any object which is changing its position with respect to a reference point with time is said to be in motion. This is True. Statement three: one kilometre equals one hundred centimetres. This is False, because one kilometre equals one thousand metres, which is one lakh centimetres.
Question three: Which of the following is not a standard unit of measuring length? The options are millimetre, centimetre, kilometre, handspan. The correct answer is handspan, because it varies from person to person.
Question four: Search for different scales or measuring tapes at your home and school. Find out the smallest value that can be measured using each. For example, a standard fifteen centimetre scale measures down to one millimetre. A tailor's tape usually measures down to one millimetre or half a millimetre. A metre scale in a lab might measure down to one millimetre.
Question five: Suppose the distance between your school and home is one point five kilometres. Express it in metres. We know one kilometre equals one thousand metres. So, one point five kilometres equals one point five multiplied by one thousand, which is one thousand five hundred metres.
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Question six: Take a tumbler or a bottle. Measure the length of the curved part of the base of glass or bottle and record it. You would place a thread along the curved edge, mark the ends, straighten the thread, and measure it with a scale. The recorded value will depend on your specific bottle, for example, twenty five centimetres.
Question seven: Measure the height of your friend and express it in metres, centimetres, and millimetres. Suppose the height is one hundred twenty centimetres. In metres, it is one point two metres. In centimetres, it is one hundred twenty centimetres. In millimetres, it is one thousand two hundred millimetres.
Question eight: You are given a coin. Estimate how many coins are required to be placed one after the other lengthwise, without leaving any gap between them, to cover the whole length of the chosen side of a notebook. Verify your estimate by measuring the same side of the notebook and the size of the coin using a fifteen centimetre scale. For example, if the notebook side is twenty centimetres and the coin diameter is two centimetres, you would need ten coins. You verify by actually placing them and measuring.
Question nine: Give two examples each for linear, circular and oscillatory motion. Linear motion: a car moving on a straight highway, a train moving on straight tracks. Circular motion: blades of a ceiling fan, a stone tied to a string being whirled. Oscillatory motion: a pendulum of a clock, a child on a swing.
Question ten: Observe different objects around you. It is easier to express the lengths of some objects in millimetres, some in centimetres and some in metres. Make a list of three objects in each category. For millimetres: thickness of a coin, diameter of a pencil lead, thickness of a mobile phone. For centimetres: length of a pencil, width of a book, length of a spoon. For metres: height of a door, length of a classroom, length of a bed.
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Question eleven: A rollercoaster track is made in the shape shown in Figure five point nineteen. A ball starts from point A and escapes through point F. Figure five point nineteen shows a track starting at A, going down a straight slope to B, curving into a loop from C to D, going up and down hills from D to E, and exiting straight at F. Identify the types of motion of the ball on the rollercoaster and corresponding portions of the track. From A to B, it is linear motion. From C to D in the loop, it is circular motion. From D to E over the hills, it is a combination of linear and oscillatory like motion. From E to F, it is linear motion.
Question twelve: Tasneem wants to make a metre scale by herself. She considers the following materials for it, plywood, paper, cloth, stretchable rubber and steel. Which of these should she not use and why? She should not use cloth or stretchable rubber because they can stretch or shrink, which would give incorrect and non standard measurements. A scale must be rigid and non stretchable.
Question thirteen: Think, design and develop a card game on conversion of units of length to play with your friends. You can create cards with values in one unit on one side and the converted value in another unit on the other side, or match cards like one thousand millimetres with one metre.
Now let us move to the Learning further section. Can you find the thickness of a single page of your notebook or textbook using a scale? Think of a way and write it. Carry out the activity and report your result. You can stack one hundred pages together, measure the total thickness with a scale, and then divide by one hundred to find the thickness of a single page. For example, if one hundred pages measure ten millimetres, one page measures zero point one millimetres.
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Collect fallen leaves from the same tree. Identify the name of the tree whose leaves you have taken. Measure length and breadth of all these leaves using a fifteen centimetre scale, as shown in Figure five point twenty. Figure five point twenty shows a leaf placed on a scale with a ruler measuring its longest length and widest breadth. Record your observations in a table with columns for serial number, name of tree, length of leaf, and breadth of leaf. Discuss why the leaves of the same tree vary in length and breadth. Leaves vary due to differences in sunlight exposure, water availability, age of the leaf, and position on the branch.
Discuss with elders in your community what units were used for measurement of length in the olden days. Also, using the internet, try to find out about the length scales found in excavations of archaeological sites in India. You might learn about units like gaz, hath, and kos, and discover that Harappan sites had standardized ivory and bronze scales.
Create a maze using lines of one centimetre, two centimetres and their combination. Part of it has been made for you in Figure five point twenty one. Figure five point twenty one shows a grid based maze with straight lines of specified lengths. Now use your imagination and expand it to a size as big as you want.
How tall am I? Stand along a wall and with the help of an adult, mark your height. Figure five point twenty two shows a child standing against a wall while an adult marks the top of their head. Repeat it every three months to maintain a height record for yourself and your siblings.
Let us design a fun method for measuring the distance between two places by using a bicycle. Attach a flexible metal strip to the spoke of the front wheel in such a manner that it hits the frame of the bicycle holding the wheel, every time it crosses it and produces a sound. Figure five point twenty three shows a bicycle wheel with a metal strip attached to a spoke, positioned to click against the frame. Now ride the bicycle slowly and count the number of times in which sound occurred. The number will give you the number of turns of your wheel made. Now measure the length of the outer boundary of the wheel using a string as done in Figure five point eight. Multiply this length by the number of turns of the wheel. This is the distance you travelled. Such methods are actually used to measure the distance for road running races. Try to find out about a Jones Counter which is attached to a bicycle wheel and is used for measuring distances. A Jones Counter is a precision mechanical device that counts wheel revolutions to measure race courses accurately.
We have covered every concept, activity, and exercise from this chapter. Remember to practice measuring objects around you and observe different types of motion in your daily life.
Thank you for listening! Keep revising and practicing. Goodbye! [CHAPTER_COMPLETE]