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PHYSICS
Measurement
11 September 2023
What is Physics?
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
Physics is the study of Matter and Energy.

This includes sub-topics like:
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General Physics
Thermal Physics
Light
Waves
Sound
Electricity
Magnetism
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Physical Quantities and SI units
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What is a Physical Quantity?
A physical quantity is a quantity that can be
measured.
It consists of a numerical magnitude and a unit.
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Physical Quantities and SI units
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The 7 base quantities and 7 base SI units are shown in
the table below.
Table 1.1 The seven base quantities and their SI units
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Physical Quantities and SI units
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All other physical quantities can be derived from these
seven base quantities. These are called derived quantities.
Some common derived quantities and units
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Derived SI Units (examples)
Quantity
unit
Symbol
Volume
cubic meter
m3
Density
kg/m3
Speed
kilograms per
cubic meter
meter per second
Newton
kg m/ s2
N
Energy
Joule (kg m2/s2)
J
Pressure
Pascal (kg/(ms2)
Pa
m/s
Physical Quantities and SI units
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Some common SI prefixes are listed in the table below.
Common SI prefixes
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Physical Quantities and SI units
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Worked Example
Donovan Bailey broke the 100 m sprint world record
at the 1996 Atlanta Olympics, with a time of 9.84 s.
In contrast, a dog runs at a speed of 30 km h–1. If
the dog chases Donovan Bailey, will the dog catch
up with him?
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Physical Quantities and SI units
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Solution
First, we calculate the average speed of Donovan Bailey.
Average
speed
=
distance
time
= 100 m
s
9.84
= 10.2
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m
s -1
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Physical Quantities and SI units
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Solution (Continued)
In order to make meaningful comparisons of speed, the units must be the
same. So Bailey’s speed should be converted to km h–1.
10.2 m s -1 = 10.2  1 m s -1
60 s
= 10.2  1 m  1 km

1s
1000 m
1 min

60 min
1h
= 36.7 km h -1
Since Bailey’s speed of 36.7 km h– 1 > 30 km h– 1, Bailey will
outrun the dog over a distance of 100 m.
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Physical Quantities and SI units
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Key Ideas



A physical quantity has a numerical magnitude and a unit.
The are seven base quantities: length, mass, time, electric
current, temperature, luminous intensity and amount of
substance.
The units of these seven base quantities are known as the
SI base units:
m, kg, s, A, K, cd, mole
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Physical Quantities and SI units
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Test Yourself
1. Express the weight of a ‘Quarter Pounder’ in grams, given that
2.205 pounds (lb) is equal to 1 kilogram (kg).
Figure 1.5 Quarter Pounder
2. The world’s smallest playable guitar is 13 m long. Express
the length in standard form.
Figure 1.6 Nanoguitar
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Physical Quantities and SI units
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Solutions
1.
1 kg
1000 g
1
1

lb = 4 lb 
1 kg
4
2.205 lb
= 113.3 g
2.
13 m = 13  10-6 m
= 1.3  10-7 m (in standard form)
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Measurement of Length
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The SI unit for length is the metre (m).
There is a wide range of lengths in the natural world.
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Measurement of Length
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Some of the common instruments that we use to
measure lengths are the:
 Metre rule
 Tape measure
 Calipers
 Vernier Calipers
 Micrometer screw gauge
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Measurement of Length
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Metre rules can measure lengths up to 1 m.
Figure 1.11 Using a metre rule to
measure the depth of a pond
Tape measures can measure lengths up to a few metres.
Figure 1.9 Tape measure
Figure 1.10 Using a tape measure
to measure the width of a pond
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
Accuracy - a measure of how close a
measurement is to the true value of
the quantity being measured.
Example: Accuracy
Who is more accurate when measuring a
book that has a true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision – a measure of how close a
series of measurements are to one
another. A measure of how exact a
measurement is.
Example: Precision
Who is more precise when measuring the same
17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the following
are precise, accurate or both.
Accurate
Not Accurate
Accurate
Not Precise
Precise
Precise
Measurement of Length
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Accuracy of an Instrument
The accuracy of an instrument is the smallest unit
that the instrument can measure.
What is the accuracy of the metre rule? The smallest
unit the metre rule can measure is 0.1 cm or 1 mm.
Hence, we say that the metre rule has a accuracy of
0.1 cm.
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Measurement of Length
Avoiding Reading Errors
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When using the metre rule, position your eye directly above the
markings to avoid parallax errors. By taking several readings and
taking the average, you will minimise reading errors.
Figure 1.12(a) No parallax errors
Figure 1.12(b) Inaccurate
measurement due to parallax errors
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Measurement of Length
Calipers – An instrument for measuring the diameters
of cylinders or circular objects.
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Figure 1.13(a) Inverting the jaws of the calipers to measure
inner diameters
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Measurement of Length
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Figure 1.13(b) Calipers used to measure outer diameters.
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Measurement of Length
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Vernier Calipers
A useful instrument to measure both internal and
external diameters of objects. It consists of a main
scale and a sliding vernier scale.
The vernier calipers has a precision of 0.01 cm.
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Measurement of Length
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Figure 1.14 Parts and uses of the vernier calipers
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For online simulation.
 http://www.stefanelli.eng.br/en/virtual-vernier-calipersimulator-05-millimeter/


https://www.stefanelli.eng.br/en/simulator-virtualmicrometer-hundredths-millimeter/
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Measurement of Length
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Using the Vernier Calipers
Before using the vernier calipers, it is important to
check the instrument for zero error.
This is to check that the zero mark on the main scale
coincides with the zero mark on the vernier scale
when not measuring anything between the jaws.
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Guide to Using Vernier Calipers
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Table 1.4 Checking and correcting zero errors when using vernier calipers
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Measurement of Length
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Micrometer Screw Gauge
This instrument can measure to a precision of 0.01
mm. It is used to measure the diameters of wires or
ball bearings.
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For online simulation.
 http://www.stefanelli.eng.br/en/virtual-verniercaliper-simulator-05-millimeter/


https://www.stefanelli.eng.br/en/simulator-virtualmicrometer-hundredths-millimeter/
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Figure 1.16 Step by step guide to using the micrometer screw gauge
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Table 1.5 Checking and correcting zero errors when using the micrometer screw gauge
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Measurement of Length
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Key Ideas
1. Instruments with their range and accuracy.
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Measurement of Length
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2. Errors to take note for each instrument
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Test Yourself 1.3
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1. Figure 1.17 shows a voltmeter with a strip of mirror
mounted under the needle and near the scale.
Suggest how this may help to reduce errors when
taking a reading.
Figure 1.17 Voltmeter scale with
mirror mounted under the needle
Answer: When taking a reading, ensure that your
vision is placed directly above the needle so that the
image of the needle coincides with the needle. This
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helps to reduce parallax error.
2. Vernier calipers are used to measure the diameter of a ball bearing.
What is the reading of the vernier scale?
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Answer:
Step 1: Main scale reading: 2.5 cmnier reading
is 0.03 cm.
Step 2: Vernier coincides with 3rd line. Ver
Step 3: Reading of diameter = 2.5 + 0.03 cm
= 2.53 cm
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3. The diameter of a wire is measured using a micrometer
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screw gauge. A student takes an initial zero reading
and then a reading of the diameter. What is the
corrected diameter of the wire in mm?
A 3.37 B 3.85 C 3.89
D 3.87
Answer:
The zero reading Z = +0.02 mm
The diameter reading D = 3.87 mm
Hence the corrected diameter reading:
Dcorrected = D – Z = 3.87 – (+0.02)
= 3.85 mm
Therefore the answer is B.
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Measurement of Time
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In this lesson, you’ll be able to:
 Describe how to measure periods of time using the
pendulum, stopwatch and other appropriate
instruments.
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Using a Pendulum to Measure Time
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A simple pendulum consists of a bob attached to a
string.
 A complete to-and-fro motion from R to S and back to R
is one complete oscillation.
 The period T is the time taken for one complete
revolution.
Figure 1.22 A pendulum completes one full oscillation when the bob moves from
R to S and back to R.
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Instruments for Telling Time
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All instruments use some kind of periodic motion to
tell time e.g. mechanical watches or clocks use the
oscillations of springs, quartz watches use the
natural vibrations of crystals.


Stopwatches can measure time to a precision of 0.1 s.
Digital stopwatches can show readings to two decimal places
of a second. However, human reaction time introduces an
error of about
0.3–0.5 s.
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Measurement of Time
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Experiment 1.1
Objective: To calibrate a simple pendulum to measure
time in seconds.
Apparatus: pendulum, stopwatch, metre rule, retort
stand and clamp
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Measurement of Time
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Procedure:
1. Fasten the metre rule vertically.
2. Tie the pendulum to the clamp
and measure the length of the
string, l in metres.
3. Measure the time taken t for the
pendulum to make 20 oscillations.
4. Vary the length l between
60 cm and 100 cm.
Figure 1.24
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Measurement of Time
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Complete the table below.
Plot a graph of period T/s against l/m and find the
length of pendulum with a period of one second.
Plot also a graph of T2/s2 against length l/m.
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Measurement of Time
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Results:
Figure 1.25(a) Graph of T/s vs. l/m
Figure 1.25(b) Graph of T2/s2 vs. l/m
The length of pendulum with a period of 1 second can be
read off the graph.
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Measurement of Time
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Question 1: Why do we need to take the average
time of 20 oscillations?
Answer: We take the average to account for human
reaction time. Human reaction time is about 0.3 s for
most people. It would not be accurate to stop a
stopwatch to measure the time taken for just one
oscillation.
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Measurement of Time
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Question 2: What can you observe about the
graph of T/s vs. l/m?
Answer: The period of the pendulum, T, increases
with length l, but not linearly.
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Measurement of Time
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Question 3: What does the plot of T2/s2 vs. l/m tell us?
Answer: It tells us that the square of the period, T2
is directly proportional to the length, l. This gives rise
to the straight line graph when we plot T2/s2 against
l/m. By extending the straight line graph, we can
easily predict the period of the pendulum for lengths
that are not included in the graph we have plotted.
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Measurement of Time
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Key Ideas

Time intervals are measured by observing events that repeat themselves.

Clocks can be used to measure time intervals in minutes or hours.

Stopwatches can be used to measure time intervals to a precision of 0.1 s.

The period T is the time taken for the pendulum to swing from one end to the
other and back again to its starting position.
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Measurement of Time
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Test Yourself 1.4
1. How can you measure the average time taken by a bus to travel from home to
school?
Answer: At the beginning of the week e.g. Monday,record
the time on your watch when you board the bus. Record the
time when you alight the bus. The difference between the
two times is the time taken for the journey. Repeat steps
2-3 over the course of the week until Friday. Take the
average of the time taken during the journey over the 5 days.
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Measurement of Time
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2. How can you determine the period of the swing in the playground?
Answer: Start the swing in its to-and-fro motion.
When the motion is steady, start the stopwatch when
the swing is at one end of its motion. Stop the
stopwatch after 20 oscillations. Record the time t1.
Repeat steps 2-3 for another set of reading t2.
(t1 + t2)
Take average t =
2
t
20
The period T is given by T =
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Measurement of Time
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3. Figure 1.26 shows an oscillating pendulum. If the
time taken for the pendulum to swing from A to C
to B is 3 s, what is the period of the pendulum?
Answer:
Moving from A to C to B only
covers three-quarters of the
oscillation. Hence,
3T=3s
4
4 =4s
T = 3 
3
Figure 1.26
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