Chapter

5 Measurement of Length
and Motion

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 (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, Tasneem and this leads to a
discussion amongst them.

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 Anish Hardeep Padma

Deepa Tasneem

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,”
Curiosity | Textbook of Science | Grade 6

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.”
for measuring

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 Table 5.1: Measuring the length of the table

Name of the Student Number of Handspans

Anish Slightly more than 13

Padma 13

Tasneem Slightly less than 13

Deepa Between 13 and 14

Hardeep 14

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
Measurement of Length and Motion

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.
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 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
More to excavated from sites of the Harappan
know! 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
Curiosity | Textbook of Science | Grade 6

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
Fig. 5.2:
marks, such as between 1 and 2 or between A metre scale
5 and 6, is 1 cm. Observe that these sections
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 Fig. 5.3: A 15-cm scale

of 1 cm length are further divided

into 10 equal parts. The length of
one of these smaller parts is called
Would it be convenient to use
a millimetre (mm). 1 mm is the
the unit metre to measure
smallest value of length that you

?
larger lengths, such as the
can measure using this scale. 1 mm
length of a railway track
is equal to one-tenth of a centimeter
between two cities, or to
(1 mm = 0.1 cm).
measure smaller lengths,
For measuring larger lengths, we
such as the thickness of a
use a larger unit called a kilometre
page of a book?
(km) which is equal to 1000 metres.
And for measuring smaller lengths,
we use units such as centimetre or
millimetre.

1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm

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
Measurement of Length and Motion

some people.

Do you
know?

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 re
o s e w e all measu
Sup p le
of the tab
the length sing No, bu
, b u t th is time u t we sh
again l our first le ould
cale. Wil arn th
a metre s ent? way of e corre
u lt s s ti ll be differ using a ct
res to mea scale
sure le
ngth.

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.
Curiosity | Textbook of Science | Grade 6

(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).
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 B
A C

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.

Measurement of Length and Motion

Fig. 5.6: Correct method of placing the scale with broken end

How do visually challenged students measure lengths?

They use scales with raised markings that can be felt by
touching them.

Do you
know?
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 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.
Table 5.2: Measuring lengths

Object Length of the object

Why are s While writing the length, do not forget

ome
length me
asuring to write the unit also. Thus, your result
devices m
ade will consist of two parts—one part is a
up of flex number and the other part is the unit of
ible
materials 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.
Curiosity | Textbook of Science | Grade 6

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
Do you
number and the unit.
know?
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 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 Measurement of Length and Motion

feel that the school would be closer, Hardeep thinks that

both would be almost at an equal distance (Fig. 5.9).
Deepa’s Anish’s Hardeep’s Tasneem’s Padma’s
Bus stand School Garden
house house house house house

Fig. 5.9: Location of bus stand, school, garden and houses of Deepa and her friends
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 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
Fig. 5.10: point.” (Fig. 5.11)
A measuring tape

Reference
Point
Curiosity | Textbook of Science | Grade 6

Fig. 5.11: Drawing lines for Kabaddi 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 70 km’ (Fig. 5.12).
Further on, the next kilometre stone
read ‘Delhi 60 km’. Each kilometre stone
Fig. 5.12: indicated that she was getting closer to her
A kilometre stone
grandparents’ house.

?
These kilometre stones indicated
What do such
her distance from Delhi. So, Delhi is
kilometre stones
the reference point in this situation.
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

If the kilometre stone reads ‘Delhi 70 km’ as shown in

Fig. 5.13, we can say that the position of Padma is 70 km
from Delhi. When the kilometre stone reads ‘Delhi 60 km’,
the position of Padma is 60 km from Delhi.
Measurement of Length and Motion

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?

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 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

Objects in Objects at
Justification Justification
motion rest

Cow grazing
Tree
in the field
Curiosity | Textbook of Science | Grade 6

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.
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 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. More to
know!

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
Think it on the ship. Is there any way that you can
over! determine whether the ship is moving or is
stationary?

5.7 Types of Motion

Activity 5.3: Let us explore Measurement of Length and Motion

‹‹ 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).
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 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) to one end of a thread.
Curiosity | Textbook of Science | Grade 6

‹‹ 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-go-
round?
When an object moves along a circular path, its motion is
called circular motion.

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 Fig. 5.15: Circular motion

Activity 5.5: 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
(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.

Measurement of Length and Motion

Fig. 5.16: Oscillatory motion

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 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

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
More to moving to and fro. Both circular and oscillatory motion are
periodic in nature.
know!
Curiosity | Textbook of Science | Grade 6

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.
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 Fig. 5.18: Types of motion observed in a children’s park

Table 5.4: Types of Motion

Linear Circular Oscillatory

Object
motion motion motion
Measurement of Length and Motion

Swing Moving to and fro

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 Keywords

centimetre Measurement Classify

Circular motion metre Explore

Distance millimetre Identify

kilometre Motion Investigate

Length Oscillatory motion Justification

Linear motion Reference point Observe

SI Unit of Length

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
Curiosity | Textbook of Science | Grade 6

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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 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

Column I Column II

Distance between Delhi and

centimetre
Lucknow

Thickness of a coin kilometre

Length of an eraser metre

Length of school ground millimetre

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 [ ] Measurement of Length and Motion

3. 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.
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 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

Size Objects

mm

cm

m
Curiosity | Textbook of Science | Grade 6

11. A rollercoaster track

is made in the shape A
shown in Fig. 5.19. D
A ball starts from
point A and escapes
through point F. E
Identify the types of F
B
motion of the ball
on the rollercoaster C
and corresponding
portions of the track. Fig. 5.19: Rollercoaster track

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 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

Length Breadth
Measurement of Length and Motion

S. no. Name of tree

of leaf of leaf

1.

Discuss why the leaves of the same tree vary in length

and breadth.

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 ‹‹ 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.
‹‹ How tall am I? Stand along
Fig. 5.21: A maze 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.
‹‹ 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 Fig. 5.22: Measuring height
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
Curiosity | Textbook of Science | Grade 6

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

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