Measurement of Length and Motion — Class 6 Science
Curiosity · Chapter 5
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5- Mathematics
- Science
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Chapter summary
Key ideas & terms
- Standard unit
- A fixed unit of measurement, such as the metre, that gives the same result no matter who measures the same length.
- SI unit of length
- The metre (m); 1 km = 1000 m, 1 m = 100 cm, and 1 cm = 10 mm.
- Reference point
- A fixed object or point with respect to which the position of an object is stated.
- Motion and rest
- An object is in motion if its position changes with respect to a reference point with time, and at rest if its position does not change.
- Linear motion
- Motion of an object along a straight line.
- Circular and oscillatory motion
- Circular motion is along a circular path, while oscillatory motion is a to-and-fro movement about a fixed position; both are periodic.
Extra questions & answers
Why can body parts like a handspan not be used as reliable units of length?
Because body parts such as the handspan, foot, or fingers differ in size from person to person, so the same length measured by different people gives different numbers.
What is the SI unit of length, and what are its common relations?
The SI unit of length is the metre (m); 1 km = 1000 m, 1 m = 100 cm, and 1 cm = 10 mm.
What is the correct position of the eye while reading a scale?
The eye should be directly above the point being read, in line with the mark, to avoid errors in measurement.
How do you measure length when the zero end of the scale is broken?
Place a full mark, such as 1.0 cm, at one end and subtract its reading from the reading at the other end; for example, 10.4 cm minus 1.0 cm gives a length of 9.4 cm.
How can the length of a curved line be measured?
A curved line can be measured using a flexible measuring tape, or by laying a thread along the curve, then straightening the thread and measuring it with a metre scale.
What is a reference point?
A reference point is a fixed object or point with respect to which the position of an object is stated, such as a city marked on kilometre stones.
When is an object said to be in motion?
An object is in motion if its position changes with respect to a reference point with time; if its position does not change, it is at rest.
How can the same object be both at rest and in motion?
It depends on the reference point: a bus passenger is at rest relative to the bus but in motion relative to a building outside, because position depends on the chosen reference.
What are the three types of motion described in the chapter?
Linear motion (along a straight line), circular motion (along a circular path), and oscillatory motion (to and fro about a fixed position).
Why are circular and oscillatory motion called periodic?
Because the object repeats its path after a fixed interval of time — moving along the circle again and again, or repeating the to-and-fro movement.
Activity 5.1: Let us measure
Select some objects around you, such as a comb, a pen, a pencil, and an eraser to measure their lengths.
Choose objects easily found in your geometry box. Place each object along a metre scale so that one end is at the
Measure their lengths one by one using a metre scale and note down the measurements in Table 5.2.
Using the correct placement of the scale and eye position, measure each object and write the result as a number plus a unit, for example: comb —
Activity 5.2: Let us explore
Look around and prepare a list of five objects that are in motion and five objects that are at rest.
With a classroom or playground as the reference point, objects in motion could be: a walking student, a rolling ball, a ceiling fan blade, a swinging pendulum, flowing water. Objects at rest could be: a desk, a blackboard, a tree, a school building, a bag on the floor. Motion is decided relative to a chosen reference point.
Record your observations in Table 5.3.
Create two columns in Table 5.3. In the 'Objects in motion' column list the five moving objects and in the 'Objects at rest' column list the five stationary objects observed from the same reference point, for example classroom floor.
Think about how you decided whether an object was in motion or at rest. Write your explanation (justification) in Table 5.3.
Justification: An object is in motion if its position changes with time with respect to the chosen reference point, and at rest if its position does not change with time with respect to that same reference point. For example, a ball changes its distance from the desk as time passes, so it is in motion, while the desk keeps the same distance from the wall, so it is at rest.
Activity 5.3: Let us explore
Take an eraser and drop it from a certain height.
Hold an eraser about
Observe its motion.
The eraser falls straight down towards the ground. Its path is a straight line, so this is an example of linear motion. The same straight-line motion is seen when an orange drops from a tree or when students march in a straight line.
Activity 5.4: Let us investigate
Tie an eraser (or a potato) to one end of a thread.
Take a strong thread about
Hold the other end of the thread with your hand and whirl it (Fig. 5.15).
Hold the free end firmly between your fingers, extend your arm, and rotate your hand in a horizontal circle so the eraser moves in a circular path around your hand. Keep the motion steady and safe.
Observe its motion.
The eraser moves continuously along a circular path with your hand as the centre. This is circular motion. It is similar to a merry-go-round where each seat moves in a circle.
Activity 5.5: Let us investigate
Tie an eraser (or a potato) to one end of a thread.
Knot the thread tightly around the eraser, leaving about
Hang the eraser by holding the other end of the thread (Fig. 5.16). Keep your hand steady.
Hold the free end fixed at a point so the eraser hangs vertically without touching anything. Wait until it comes completely to rest.
Using the other hand, take the eraser slightly to one side and then release (Fig. 5.16).
Pull the hanging eraser a few centimetres to one side and let go gently without pushing. Do not move the hand that holds the thread.
Does it start moving to and fro? Is its motion similar to the motion of a swing?
Yes, the eraser swings to and fro about its central rest position. This to-and-fro motion about a fixed position is called oscillatory motion and is exactly like the motion of a child on a swing.
Activity 5.6: Let us investigate
Take a thin metal strip of about 50 cm long.
Use a thin, flexible metal ruler or strip about
Hold its one end pressed to a table. You may use a few books or a brick to hold it (Fig. 5.17).
Place about
Press the free end of the strip slightly and let it go.
Gently push the free end down by
Observe the motion of this end of the strip.
The free end vibrates up and down rapidly about its original position before slowly coming to rest. This up-and-down motion about a fixed position is also oscillatory motion, and because it repeats after a regular interval it is also periodic.
Activity 5.7: Let us identify
Look at the picture of a children’s park (Fig. 5.18) or visit a children’s park.
Observe the park carefully. Note the swing, the merry-go-round, the slide, the seesaw, and children running on a straight path.
Observe different kinds of motions. Classify them as linear, circular or oscillatory motion.
Swing and seesaw: oscillatory motion because they move to and fro about a fixed point. Merry-go-round and the rotating wheel: circular motion because they move along a circular path. Children sliding down a straight slide or running straight: linear motion because they move along a straight line.
List them in Table 5.4. Give your justification for why you put each in a certain category.
In Table 5.4 write: Swing — oscillatory — moves to and fro about mean position; Merry-go-round — circular — moves repeatedly along a circle; Slide — linear — moves along a straight line; Seesaw — oscillatory — goes up and down about the pivot. Justification is based on whether the path is straight, circular, or to-and-fro about a fixed position, and whether the motion repeats periodically.
Let us enhance our learning
Distance between Delhi and Lucknow
kilometre
Thickness of a coin
millimetre
Length of an eraser
centimetre
Length of school ground
metre
2. Read the following statements and mark True (T) or False (F) against each. (i) The motion of a car moving on a straight road is an example of linear motion. [ ]
True
2. Read the following statements and mark True (T) or False (F) against each. (ii) Any object which is changing its position with respect to a reference point with time is said to be in motion. [ ]
True
2. Read the following statements and mark True (T) or False (F) against each. (iii) 1 km = 100 cm [ ]
False
3. Which of the following is not a standard unit of measuring length? (i) millimetre (ii) centimetre (iii) kilometre (iv) handspan
(iv) handspan is not a standard unit. Millimetre, centimetre and kilometre are part of the International System of Units
4. Search for the different scales or measuring tapes at your home and school. Find out the smallest value that can be measured using each of these scales. Record your observations in a tabular form.
Check a 15-cm plastic scale, a 1-m wooden metre scale, a tailor’s flexible tape and a long measuring tape. On a typical 15-cm scale the smallest division is
5. Suppose the distance between your school and home is 1.5 km. Express it in metres.
Since
6. Take a tumbler or a bottle. Measure the length of the curved part of the base of glass or bottle and record it.
Wrap a thread tightly around the circular base, mark where the thread meets, then straighten the thread and measure its length against a metre scale. This length is the circumference. For a typical tumbler it may be about
7. Measure the height of your friend and express it in (i) metres
Make your friend stand straight against a wall, mark the top of the head, and measure the distance from the floor to the mark. Suppose the measured height is
7. Measure the height of your friend and express it in (ii) centimetres
Using the same measurement, the height is
7. Measure the height of your friend and express it in (iii) millimetres
Since
8. 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 15-cm scale.
First estimate by eye, for example you may guess 12 coins. Then measure: suppose the long side of the notebook is
9. Give two examples each for linear, circular and oscillatory motion.
Linear motion: (1) a car moving on a straight road, (2) a box being pushed along a straight floor. Circular motion: (1) a merry-go-round rotating, (2) the tip of a ceiling fan blade moving in a circle. Oscillatory motion: (1) a child swinging on a swing, (2) the vibration of a pressed metal strip fixed at one end. Circular and oscillatory motions are also periodic because they repeat after a fixed time.
10. Observe different objects around you. It is easier to express the lengths of some objects in mm, some in cm and some in m. Make a list of three objects in each category and enter them in the Table 5.6.
In mm — thickness of a coin
11. A rollercoaster track is made in the shape shown in Fig. 5.19. A ball starts from point A and escapes through point F. Identify the types of motion of the ball on the rollercoaster and corresponding portions of the track.
Portion A to B which is straight inclined: linear motion. Portion B to C and D to E which are curved circular loops: circular motion. Portion C to D which is like a dip where the ball may swing to and fro if it oscillates, but mainly circular/linear; if the track has a bumpy section it can show oscillatory motion. Overall the ball shows linear motion on straight sections and circular motion on curved sections, and if it goes back and forth in a valley it can also show oscillatory motion. Each repeating loop is also periodic.
12. 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 and stretchable rubber. These materials can stretch, shrink or fold, so their length changes with pulling or with temperature and humidity. A scale must keep a fixed length, which plywood, paper pasted on wood, or steel can provide because they do not stretch easily and remain stable.
13. Think, design and develop a card game on conversion of units of length to play with your friends.
Make two sets of cards: one set with values like
Learning further
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.
A single page is too thin to measure directly with a scale whose least count is
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 15-cm scale, as shown in Fig. 5.20. Record your observations in the Table 5.7. Discuss why the leaves of the same tree vary in length and breadth.
Example: Neem tree — leaf 1: length
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.
Elders often recall non-standard units like angula (finger width), balisht or handspan, haath (cubit, from elbow to fingertip), footstep or stride, and gaj. In ancient India, angula, dhanusa and yojana were used for architecture and town planning. Archaeologists have found ivory and shell scales with ruled markings at Harappan sites like Mohenjodaro and Lothal, showing that standardized length measurement existed thousands of years ago.
Create a maze using lines of 1 cm, 2 cm and their combination. Part of it has been made for you in Fig. 5.21. Now use your imagination and expand it to a size as big as you want.
On a sheet of paper, draw horizontal and vertical walls using only segments of
How tall am I? Stand along a wall and with the help of an adult, mark your height (Fig. 5.22). Repeat it every three months to maintain a height record for yourself and your siblings.
Stand barefoot with heels touching the wall, head straight. Place a book flat on the head and mark the wall at that level. Measure from the floor to the mark with a metre tape, for example
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 (Fig. 5.23). 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 Fig. 5.8. Multiply this length by the number of turns of the wheel. This is the distance you travelled.
First measure the circumference of the wheel with a thread: wrap the thread around the outer edge, straighten and measure, suppose