PHYSICAL QUANTITIES AND MEASUREMENT

DBS 10012

ENGINEERING SCIENCE

CHAPTER 1 :
PHYSICAL QUANTITIES AND

MEASUREMENT

Physical Quantities

• defined as a quantity that can be measured

• Examples

length, mass, time, volume, density, current, force

Physical Quantities

There are 2 types of physical quantities

defined as a Base (Basic) Derived defined as a
quantity quantities quantities quantity which can
which be derived from

cannot be base quantity
derived whether by
from any
physical multiplication
quantities operational or
division operation

or both.

Physical Quantities

Base • Current
(Basic) • Mass
quantities • Time
• Length
• Temperature
• Amount of substance
• Brightness (light intensity)

Base Quantities

Base quantity Symbol SI Unit Unit Measurement Apparatus
Abbreviation
Current I ampere Ammeter
Mass m kilogram A Beam balance
Time t Seconds Kg
Length l Meter S Stop watch
Temperature T Kelvin m Meter ruler
K Thermometer

Amount of a - mole mol No measuring devices which
substance directly measure moles.

Brightness - candela cd Luminous Flux/Lumen
(light intensity)

Physical Quantities

Derived • Force
• Density

Quantities • Pressure
• Volume

• Area

• Acceleration

Derived Quantities

Derived quantity Symbol Terms of base Derived unit SI unit
Force F quantities Kgms-2
Power P Kg x ms-2 −1 or watt
Pressure P −2
Density p
Velocity v kgm-3
2 ms-1
acceleration a
Area A 3 Ms-2
m2


ms−1



m xm



Scalars & Vectors

A scalar quantity has only magnitude

• Length, area , speed, mass , density.

A vector quantity has both magnitude and direction

• Acceleration, velocity, weight , force, momentum , displacement

Measurement & Errors in Measurement

Measurement Errors

can be defined as a number Can be defined as the
that shows the size or difference between the actual
amount of something which value of a quantity and the
is measured in standard unit value obtained by a
such as a meter or kilogram measurement.
or etc.

Measurement & Errors in Measurement

Consistency, Accuracy and Sensitivity

In every measurement when we use the
instruments, sometimes the tool gives
the wrong readings. This is because of

the consistency, accuracy and
sensitivity occurs in readings

Consistency, Accuracy and Sensitivity

Consistency Accuracy Sensitivity

• is also known as • can be defined • can be defined as
precision (in some as the the ability of the
reference books) approximation tool to detect
of the small changes in
• can be defined as the measurement to measured quantities
ability of the the actual value of physics
measuring device to for a certain
produce a consistent quantity of
reading with little or no physics.
relative deviation
between the readings
obtained.

Consistency, Accuracy and Sensitivity

The pictures of the differences between accuracy and consistency are shown below
Accurate and Consistent

Not Accurate but Consistent
Accurate but Not Consistent

Not Accurate and Not Consistent

• The Errors in Measurement of the

accuracy, consistency and sensitivity
instruments that we used to measure tools are being
influenced and affected by different types of errors

2 types of Random
Errors Errors
Systematic
Errors

* These errors also known as experimental errors

Random Errors

Random errors Errors
are the or caused by
uncertainty of individual
measurement
caused by the error
observer during
measurement reads.

Source Of Random Errors

Counting’s Parallax *Natural
error error error

Due to Reading position The ambient
mistake in of the observer is temperature
counting changes during the
not experiment or
perpendicular to wind circulation
the reading scale

*Natural Natural errors are caused by
error environmental conditions or
significant changes in environmental
conditions.

Wind speed, air temperature,
atmospheric pressure, humidity,
gravity, earth curvature, and
atmospheric refraction are
examples of natural error sources.

How to reduce Random Errors?

Can be Repetition Averaging
reduced of readings the

by readings

Systematic Errors

• These The conditions of the
errors are instruments or because
of the *environmental
caused errors while taking the
by
readings.

For examples ?? Students give the ideas…

*Environmental The environmental errors occur due to
errors some external conditions of the
instrument. External conditions mainly
include pressure, temperature, humidity or
due to magnetic fields.

In order to reduce the environmental
errors :
• Try to maintain the humidity and

temperature constant in the laboratory
by making some arrangements.

• Ensure that there shall not be any
external electrostatic or magnetic field
around the instrument.

Source of Systematic Errors

Zero error Improper use Errors from Wrong
of instrument instruments assumptions
• Tool’s
reading • Instrument is • The tools • Using the
should be wrongly used can not wrong
zero but it by the calibrated value in
gives a experimenter correctly calculation
non-zero
value.

How to reduce Systematic Errors?

Can be
reduced by

Improving the
measurement method

used

Using more precise and
accurate measuring tools

The more proficient
people who take the

reading

Unit Conversion

• Metric units
• Customary units

Physical Quantities Metric Units Customary Units

Length Kilometer (km) Inch (in)
Meter (m) Foot (ft)
Centimeter (cm) Feet (ft)
Milimeter (mm) Yard (yd)

Weight and mass Kilogram (kg) Ounce (oz)
Volume and capacity Gram (g) Pound (Ib)
Milligram (mg) Ton (T)
Temperature
Liter (L) Gallon (gal)
Mililiter (ml) ft3
m3 yd3

Kelvin (K) Fahrenheit (F)
Celsius (oC)

The following table shows the relationship
between metric and customary units

Length

1 inch (in) 2.54 centimetres (cm)

1 foot (ft) 12 inches (in) 30.48 centimetres (cm)
1 yard (yd) 3 feets (ft) 0.9144 metres (m)
1 mile (mi) 1.60934 kilometres (km)
1 760 yards (yd)
1 ounce (oz) Mass (weight) 28.35 grams (g)

1 pound (Ib) 453.59 grams (g)

Area

1 in2 6.4516 cm2

1 ft2 0.09 m2

1 yd2 9 ft2 0.8361 m2

1 acre 4 840 yd2 4046.86 m2

1 mile2 640 acres 2.590 km2

Volume

1 gallons (gal) 3.8 litres (L)

1 ft3 0.03 m3

1 yd3 0.76 m3

Temperature Conversion

Convert Fahrenheit (F) to Celcius (C) (degrees F – 32) x 0.555

Convert Celcius (C) to Fahrenheit (F) (degrees C x 1.8) + 32

Prefixes Prefix Symbol Multiplication Factor
Tera T ×
Giga G ×
Mega M ×
Kilo k ×
Hecto h ×
Deca da ×
Deci d × −
Centi c × −
Mili m × −
Micro µ × −
Nano n × −
Pico p × −

Examples of convert units :

• i) Convert 35 km to m

= 35 × 1000 =
1

• ii) Convert 286 ft to yd

= 286 ft × 1 yd = 286 ft × 1 yd = .
3 ft 3 ft

Examples of convert units :
• iii) Convert 0.26 gal to litre (L)

= 0.26 gal × 3.8 L = 0.26 gal × 3.8 L
1 gal 1 gal
= .

• iv) Convert 30.2 m3 to cm3

= 30.2 3 × 100 × 100 × 100
1 1 1

= . ×

Exercises : Conversion Units 1

• 1. Convert the following metric units : ANSWERS
• A) 10 hours to second
• B) 15 3 to c 3 1. A) 36 000 s
• C) 200 kg/ 3 to / 3 B) 15 000 000 c 3
• D) 160 km/h to m/s C) 0.2 / 3
• E) ½ day to second D) 44.44 m/s
• F) 250 000 µm to km E) 43 200 s
F) 0.00025 km

Exercises : Conversion Units 2

• 2. Convert the following customary units:

• A) 55 yard to mile ANSWERS

• B) 300 feets to yard 2. A) 0.03125 mi
• C) 6 acres to yard2 B) 100 yd
• D) 20 inches to foot C) 29 040 yd2
• E) 350C to Fahrenheit D) 1.67 ft
E) 95 F

Exercises : Conversion Units 3

• 3. Convert the following customary-metric units:

• A) 8.5 ft to metre ANSWERS
• B) 5 in to cm
• C) 0.25 litres to gallon 3. A) 2.5908 m
• D) 80 acres to km2 B) 12.7 cm
• E) 20 pound to gram C) 0.0658 gal
D) 0.3237 km2
E) 9071.8 g

Interpret Readings of Measurement Tools

Vernier Caliper• It is more sensitive • It is used to
Micrometer Screwthan meter rulemeasure even
Gauge smaller dimensions
• Generally a vernier than the vernier
caliper is in callipers
centimetres (cm)
unit but sometimes • This tool is exist in
also in inches (in) or millimetres unit
millimetres (mm) only
unit.

Vernier Caliper

For the main scale on the common
vernier caliper is probably 0.1 cm.

 With the vernier scale commonly is
0.01 cm accuracy

Functions of Vernier Caliper

Measure the thickness Measure the length of
of work pieces an object

Vernier caliper is used to :

Measure the depth of Measure the diameter
holes of the circle diameter

Taking Reading from a Vernier Caliper :

Reading of vernier caliper = Reading of main scale
+

Reading of vernier scale.

• Example : Determine the reading of red mark on a
vernier caliper below Answer :

Reading = Main scale + vernier scale
= 0.3 cm+ (0.58 mm)
= 3.58 mm or 0.358 cm

Zero Errors for Vernier Caliper

The zero error is determined by tightening the jaws of the vernier
caliper and it must be eliminated from the reading. To find the actual
reading, we used the following formula :

Actual Reading = Reading of Vernier Caliper - Zero Error

Zero errors can be categorized into two types:

• A) Positive zero error
• B) Negative zero error

Vernier caliper : Non-zero error

When the jaws are tight
closed together, then vernier
caliper gives the reading as
shown as picture beside, it
means that there is
non-zero error

Vernier Caliper : Positive Zero Error

Vernier scale and main
scale is not coincide after
the jaws closed

Coincide scale = + 0.02 cm

Vernier Caliper : Negative Zero Error

Vernier scale and main
scale is not coincide after
the jaws closed

Coincide scale ** Noted : There are 2 methods to read
the negative zero errors

Method 1 : Read from the back of vernier scale

The value for
negative zero error is
- 0.06 cm

Coincide scale

Method 2 : Read from the front of vernier scale

The value for negative
zero error is
0.1 – 0.04 = 0.06 cm

Coincide scale Therefore, negative zero
error is - 0.06 cm

Why do we use 0.1 ??

It is because the
accuracy of main scale
is 0.1 cm = 10 division
of vernier scale

Examples of zero errors

1. Figure (a) shows the reading of a vernier caliper and figure (b) is
its zero error. Determine the actual reading of vernier caliper

Solution :

Actual Reading = Reading of Vernier Caliper - Zero Error

Answer :

Actual Reading = Reading of Vernier Caliper - Zero Error

=? + ?
=
= 3.38 cm

Example of zero errors

2. Calculate the actual reading of a vernier caliper if its
readings are shown below :

Main scale 2.8 cm
Vernier scale 0.08 cm
Zero error + 0.02cm

Solution : ???

Answer : 2.86 cm

Micrometer Screw Gauge

• Micrometer screw gauge is used to to measure the

length or thickness of a small body with a high
precision.

• It has a higher precision than the vernier calipers.

Taking Reading from Micrometer Screw Gauge

Reading of micrometer = Reading of main scale
+

Reading of thimble scale.

• Example : Determine the reading of a micrometer screw
gauge below
Answer :

Reading = Main scale + vernier scale
= 6.0 + 0.42
= 6.42 mm

Zero Errors for Micrometer Screw Gauge

Actual Reading = Reading of Micrometer Screw Gauge - Zero Error

Zero errors can be categorized into two types:

• A) Positive zero error
• B) Negative zero error

Micrometer Screw Gauge : Zero Errors

Non-zero error Positive zero error Negative zero error

Reading : Reading : Reading :
No error + 0.02 - 0.03

Examples of zero errors

1. Figure (a) shows the reading of a micrometer screw gauge and
figure (b) is its zero error. Determine the actual reading of
micrometer screw gauge

Answer :

Actual Reading = Reading of Micrometer Screw Gauge - Zero Error

Actual Reading = (2.5 + 0.37) – (+ 0.02)
= ?????
= 2.85 mm

2. Given the reading of the micrometer screw gauge is 2.54 mm but
this tool has zero error as shown in the picture below. Then
determine the actual reading of the micrometer screw gauge.

Answer :

Actual Reading = Reading of Micrometer Screw Gauge - Zero Error

Actual Reading = ????
= ?????
= 2.57 mm