10. Motion and Measurement of Distances

Introduction: How wide is this desk? How far is it from Delhi to Mumbai? In ancient times, people used foot steps or handspans to measure. But everyone's foot size is different! So, we needed a standard system.

Measurement and Units

Measurement: Comparison of an unknown quantity with some known fixed quantity. The known fixed quantity is called a Unit.

Non-Standard Units: Handspan, Cubit (elbow to fingertip), Footstep, Angul (finger width). These vary from person to person.
Standard Units: In 1790, French created the Metric System. Now we use SI Units (International System of Units).
- SI unit of length is Metre (m).
- 1 Metre = 100 Centimetres (cm).
- 1 Centimetre = 10 Millimetres (mm).
- 1 Kilometre = 1000 Metres (m).

ACTIVITY 1: Confusion

Observation: If you measure a table with your handspan and your friend measures with theirs, the number of handspans will be different. This causes confusion!

Correct Measurement of Length

Place the scale in contact with the object along its length.
If the "0" mark is broken, start from "1.0 cm" mark. Subtract 1.0 from the final reading.
Important: Your eye must be exactly in front of the point where the measurement is to be taken (Vertically above). Looking from side gives wrong reading (Parallax error).

ACTIVITY 4: Curved Line

Measuring text: Can you measure a curved line with a scale? No! Use a thread. Place the thread along the curve, then straighten it and measure the thread length with a scale.

Types of Motion

Motion: When an object changes its position with time.

Rectilinear Motion: Motion along a straight line. (e.g., Use of scale, Soldiers in a march past, Car on a straight road, Stone falling down).
Circular Motion: Object moves such that its distance from a fixed point remains the same. (e.g., Hands of a clock, Blades of a fan, Bullock moving around a well).
Periodic Motion: Motion that repeats itself after some period of time. (e.g., Pendulum, Swing, Branch of a tree moving in wind, Heartbeat, Strings of guitar).

SOLVED IN-TEXT QUESTION: Boojho

Q: Boojho is not sure if we can call the motion of a train on tracks as rectilinear or circular?

Ans: On a straight track, it is Rectilinear. On a curved track, it is Curvilinear (or part of Circular). The wheels also show Circular (Rotational) motion.

Chapter Summary

Different modes of transport are used to go from one place to another.
In ancient times, people used length of a foot, the width of a finger, the distance of a step as units of measurement. This caused confusion and a need to develop a uniform system of measurement.
Now, we use the International System of Units (SI units). This is accepted all over the world.
Metre is the unit of length in SI unit.
Motion in a straight line is called rectilinear motion.
In circular motion, an object moves such that its distance from a fixed point remains the same.
Motion that repeats itself after some period of time is called periodic motion.

Exercise Q1

Q: Give two examples each, of modes of transport used on land, water and air.

Land: Bus, Train
Water: Ship, Boat
Air: Aeroplane, Helicopter

Exercise Q2: Fill in the blanks

One metre is 100 cm.
Five kilometre is 5000 m.
Motion of a child on a swing is Periodic.
Motion of the needle of a sewing machine is Periodic.
Motion of wheel of a bicycle is Circular.

Exercise Q3

Q: Why can a pace or a footstep not be used as a standard unit of length?

Ans: Because the size of a pace or a footstep varies from person to person. This will lead to confusion and different measurements.

Exercise Q4

Q: Arrange the following lengths in their increasing magnitude: 1 metre, 1 centimetre, 1 kilometre, 1 millimetre.

Ans: 1 millimetre < 1 centimetre < 1 metre < 1 kilometre.

Exercise Q5

Q: The height of a person is 1.65 m. Express it into cm and mm.

Ans:
1.65 m = 1.65 x 100 cm = 165 cm.
1.65 m = 1.65 x 1000 mm = 1650 mm.

Exercise Q6

Q: The distance between Radha's home and her school is 3250 m. Express this distance in km.

Ans: 3250 m = 3250 / 1000 km = 3.250 km.

Exercise Q7

Q: While measuring the length of a knitting needle, the reading of the scale at one end is 3.0 cm and at the other end is 33.1 cm. What is the length of the needle?

Ans: Length = Final Reading - Initial Reading
Length = 33.1 cm - 3.0 cm = 30.1 cm.

Exercise Q8

Q: Write the similarities and differences between the motion of a bicycle and a ceiling fan that has been switched on.

Ans:
Similarity: Both the wheels of the bicycle and the blades of the fan show Circular Motion.
Difference: The bicycle also moves forward in a straight line (Rectilinear Motion), while the fan stays fixed at one place.

Exercise Q9

Q: Why could you not use an elastic measuring tape to measure distance?

Ans: Since the tape is elastic, it stretches. The measurement will change depending on how much you stretch it. You won't get a correct or consistent reading.

Exercise Q10

Q: Give two examples of periodic motion.

Ans:

Motion of a pendulum.
Motion of a child on a swing.
Motion of the strings of a guitar.

Key Facts and Definitions

1. Important Definitions

Motion: Change in position of an object with time.
Rest: State when position of object does not change with time.
Rectilinear Motion: Motion along a straight line.
Circular Motion: Motion along a circular path.
Periodic Motion: Motion that repeats after a time interval.

2. Units and conversions

Unit	Conversion
1 Metre (m)	100 Centimetres (cm)
1 Centimetre (cm)	10 Millimetres (mm)
1 Kilometre (km)	1000 Metres (m)

3. Ancient Units (Non-Standard)

Cubit: Length from elbow to finger tips.
Handspan: Length from thumb to little finger stretched.
Fathom: Length of outstretched arms.

These are not used now because they are not consistent.

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