Chapter 5
Measurement of Length and Motion
Deepa, a curious eleven-year old girl, lives in a
town of 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 (four fingers width)
Deepa shares her experience with her school friends
Anish, Hardeep, Padma, Tasneem and this leads to a
discussion amongst them.
5.1 How do we Measure?
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
Fig. 5.1: Use of handspan our measurements.”
Fig. 5.1: Use of handspan for measuring
Table 5.1: Measuring the length of the table
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.”
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 13 handspans, then 13 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.
More to Kow!
India has a rich history of measurement
systems dating back to ancient times. Angula
(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.
5.2 Standard Units
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 the 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 Fig. 5.2. One
metre (m) is divided into 100 equal divisions.
Each division is called a centimetre (cm). You
may be familiar with a smaller part of the
metre scale, typically 15 cm long, shown in
Fig. 5.3.
Look carefully at the 15-cm scale. It has
markings (in cm) from 0 to 15. The length
of any section between two consecutive big
marks, such as between 1 and 2 or between
5 and 6, is 1 cm. Observe that these sections of 1 cm length are further divided
into 10 equal parts. The length of
one of these smaller parts is called
a millimetre (mm). 1 mm is the
smallest value of length that you
can measure using this scale. 1 mm
is equal to one-tenth of a centimeter
(1 mm = 0.1 cm).
For measuring larger lengths, we
use a larger unit called a kilometre
(km) which is equal to 1000 metres.
And for measuring smaller lengths,
we use units such as centimetre or
millimetre.
Fig. 5.2:
A metre scale
Fig. 5.3: A 15-cm scale
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?
Do you know!
In some scales, you might have noticed another scale marking. This scale marking is in inches, where 1 inch = 2.54 cm. In earlier days, units, such as inch and foot, were used to measure length. These units are still used by some people.
5.3 Correct Way of Measuring 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 15-cm 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 Fig. 5.4.
(a) Correct
(b) Incorrect
Fig. 5.4: Method of placing the scale
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 (Fig. 5.5).
Fig. 5.5: Correct position of the eye is ‘B
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, 1.0
cm (Fig. 5.6). Then you must subtract the reading of this
mark from the reading at the other end. For example, in
Fig. 5.6, the reading at one end is 1.0 cm and at the other
end, it is 10.4 cm. Therefore, the length of the object is
10.4 cm–1.0 cm = 9.4 cm.
Fig. 5.6: Correct method of placing the scale with broken end
Do you know!
How do visually challenged students measure lengths?
They use scales with raised markings that can be felt by
touching them.
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.
- Measure their lengths one by one using a metre scale
and note down the measurements in Table 5.2.
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.
Do you know!
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.
5.4 Measuring the length of a curved line
Anish and his parents fixed electric string lights on the
arches of the verandah of their
house, as shown in Fig. 5.7, for a
celebration at home. 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 Fig. 5.8.
Fig. 5.7: House decorated with string lights
The thread can then
be straightened and its
length can be measured
using a metre scale.
Fig. 5.8: Measuring the length of a curved line
5.5 Describing Position
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 (Fig. 5.9).
Fig. 5.9: Location of bus stand, school, garden and houses of Deepa and her friends
Who do you think is correct? All of them are correct
(Fig. 5.9). 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 (limestone
powder) for making the Kabaddi court for the sports day.
”
Padma: “We will need a longer measuring tape. Let us
take it from the sports room.” (Fig. 5.10)
Deepa: “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.” (Fig. 5.11)
Fig. 5.10: A measuring tape
Fig. 5.11: Drawing lines for Kabaddi court
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 70 km’ (Fig. 5.12).
Further on, the next kilometre stone
read ‘Delhi 60 km’. Each kilometre stone
indicated to her that she was getting closer
to her grandparents’ house.
Fig. 5.12:
A kilometre stone
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?.
Fig. 5.13: Positions of kilometre stones with respect to Delhi as a reference point
Does this mean that the position of
Padma, with respect to the reference
point, is changing with time? When
does the position of an object change
with respect to a reference point? Does
it change when an object is moving?
5.6 Moving Things
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.
- Record your observations in Table 5.3.
- Think about how you decided whether an object was in
motion or at rest. Write your explanation (justification)
in Table 5.3.
Table 5.3: Observing things around you
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.
More to know!
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 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.
Think it
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?
5.7 Types of Motion
Activity 5.3: Let us explore
- Take an eraser and drop it from a certain height.
- Observe its motion.
Does it move along a straight line? When an orange drops
from the tree, does it move in a straight line? Have you seen
the Republic Day parade? Recall the march-past of students
during the parade. Do they move on a straight-line path?
When a heavy box is pushed, it may also move along a
straight line (Fig. 5.14).
When an object moves along a straight line, its motion is
called linear motion. Identify such linear motion in your
surroundings.
Fig. 5.14: Linear motion
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?
Activity 5.4: Let us investigate
- Tie an eraser (or a potato) at one end of a thread.
- Hold the other end of the thread with your hand and whirl it (Fig. 5.15).
- Observe its motion.
Is the motion of the eraser the same as that of a merry-goround?
When an object moves along a circular path, its motion is
called circular motion.
Fig. 5.15: Circular motion
Activity 5.5: Let us investigate
- Tie an eraser (or a potato) at one end of a thread.
- Hang the eraser by holding the other end of the thread (Fig. 5.16). Keep your hand steady.
- Using the other hand, take the eraser slightly to one
side and then release (Fig. 5.16).
Does it start moving to and fro? Is its motion similar to the
motion of a swing?
When an object moves to and fro about some fixed
position, its motion is called oscillatory motion.
Fig. 5.16: Oscillatory motion
Activity 5.6: Let us investigate
- Take a thin metal strip of about 50 cm long.
- Hold its one end pressed to a table. You may use a few books or a brick to hold it (Fig. 5.17).
- 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? This is also an example of
oscillatory motion.
Fig. 5.17: Oscillatory motion of a metal strip
More to know!
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.
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 different kinds of motions. Classify them as
linear, circular or oscillatory motion.
List them in Table 5.4. Give your justification for why you
put each in a certain category.
Fig. 5.18: Types of motion observed in a children’s park
Keywords
Summary
- The International System of Units (SI units) has been adopted by countries as standard units of measurement.
- The SI unit of length is metre. Its symbol is m.
- 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- 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.
Let us enhance our learning
1. Some lengths are given in Column I of Table 5.5. Some units
are given in Column II. Match the lengths with the units
suitable for measuring those lengths
Table 5.5
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. [ ]
(ii) Any object which is changing its position with respect
to a reference point with time is said to be in motion.
[ ]
(iii) 1 km = 100 cm [ ]
. Which of the following is not a standard unit of measuring
length?
(i) millimetre (ii) centimetre (iii) kilometre (iv) handspan
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.
5. Suppose the distance between your school and home is
1.5 km. Express it in metres.
6. Take a tumbler or a bottle. Measure the length of the curved
part of the base of glass or bottle and record it.
7. Measure the height of your friend and express it in
(i) metres
(ii) centimetres and (iii) millimetres.
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.
9. Give two examples each for linear, circular and oscillatory
motion.
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.
Table 5.6: Sizes of objects around us
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.
Fig. 5.19: Rollercoaster track
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?
13. Think, design and develop a card game on conversion of units of length to play with your friends.
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.
- 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.
Fig. 5.20: Measuring a leaf
Table 5.7: Length and breadth of leaves
Discuss why the leaves of the same tree vary in length and breadth.
- 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.
- 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.
Fig. 5.21: A maze
- 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.
Fig. 5.22: Measuring height
- 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. 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.
Fig. 5.23: Measuring distance