Discover PHYSICS for
GCE ‘O’ Level Science
Unit 1: Measurement
1.1 What is Physics?
• 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
Figure 1.1 What is Physics - a pictorial overview
1.2 Physical Quantities and SI units
In this section, you’ll be able to:
• understand that all physical quantities consist of a
numerical magnitude and a unit
• recall the seven base quantities and their units
• use prefixes and symbols to indicate very big or very
small SI quantities
1.2 Physical Quantities and SI units
What is a Physical Quantity?
A physical quantity is a quantity that can be measured. It
consists of a numerical magnitude and a unit.
1.2 Physical Quantities and SI units
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
1.2 Physical Quantities and SI units
All other physical quantities can be derived from these
seven base quantities. These are called derived quantities.
Table 1.2 Some common derived quantities and units
1.2 Physical Quantities and SI units
Some common SI prefixes are listed in the table below.
Table 1.3 Common SI prefixes
1.2 Physical Quantities and SI units
Worked Example 1.1
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?
1.2 Physical Quantities and SI units
Solution
First, we calculate the average speed of Donovan Bailey.
Average speed =
=
distance
time
100 m
9.84 s
= 10.2 m s -1
1.2 Physical Quantities and SI units
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
60 min
= 10.2  1 m  1 km


1s
1000 m
1 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.
1.2 Physical Quantities and SI units
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
1.2 Physical Quantities and SI units
Test Yourself 1.2
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
1.2 Physical Quantities and SI units
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)
1.3 Measurement of Length
In this section, you will be able to:
• Have a good sense of the orders of magnitude
• Describe how to measure a variety of lengths using the
appropriate instruments (e.g. metre rule, vernier
calipers, micrometer)
• Use a vernier scale
1.3 Measurement of Length
The SI unit for length is the metre (m).
Figure 1.7 There is a wide range of lengths in the natural world.
1.3 Measurement of Length
Some of the common instruments that we use to
measure lengths are the:
• Metre rule
• Tape measure
• Calipers
• Vernier Calipers
• Micrometer screw gauge
1.3 Measurement of Length
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
1.3 Measurement of Length
Precision of an Instrument
The precision of an instrument is the smallest unit
that the instrument can measure.
What is the precision 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 precision of
0.1 cm.
1.3 Measurement of Length
Avoiding Reading Errors
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
1.3 Measurement of Length
Calipers – An instrument for measuring the diameters
of cylinders or circular objects.
Figure 1.13(a) Inverting the jaws of the calipers to measure
inner diameters
1.3 Measurement of Length
Figure 1.13(b) Calipers used to measure outer diameters.
1.3 Measurement of Length
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.
1.3 Measurement of Length
Figure 1.14 Parts and uses of the vernier calipers
1.3 Measurement of Length
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.
Table 1.4 of the textbook shows how to deal with
zero errors.
1.3 Measurement of Length
Guide to Using Vernier Calipers
Figure 1.15 Using the vernier calipers to measure the diameter of a ball bearing.
1.3 Measurement of Length
Table 1.4 Checking and correcting zero errors when using vernier calipers
1.3 Measurement of Length
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.
1.3 Measurement of Length
Figure 1.16 Step by step guide to using the micrometer screw gauge
1.3 Measurement of Length
Table 1.5 Checking and correcting zero errors when using the
micrometer screw gauge
1.3 Measurement of Length
Key Ideas
1. Instruments with their range and precision.
1.3 Measurement of Length
2. Errors to take note for each instrument
1.3 Measurement of Length
Test Yourself 1.3
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
helps to reduce parallax error.
1.3 Measurement of Length
2. Vernier calipers are used to measure the diameter of a
ball bearing. What is the reading of the vernier scale?
Answer:
Step 1: Main scale reading: 2.5 cm
Step 2: Vernier coincides with 3rd line. Vernier reading
is 0.03 cm.
Step 3: Reading of diameter = 2.5 + 0.03 cm
= 2.53 cm
1.3 Measurement of Length
3. The diameter of a wire is measured using a micrometer
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.
1.4 Measurement of Time
In this section, you’ll be able to:
• Describe how to measure periods of time using the
pendulum, stopwatch and other appropriate
instruments.
1.4 Measurement of Time
Using a Pendulum to Measure Time
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.
1.4 Measurement of Time
Instruments for Telling Time
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.
1.4 Measurement of Time
Experiment 1.1
Objective: To calibrate a simple pendulum to measure
time in seconds.
Apparatus: pendulum, stopwatch, metre rule, retort
stand and clamp
1.4 Measurement of Time
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
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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.
1.4 Measurement of Time
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
The period T is given by T =
20
1.4 Measurement of Time
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=3 s
4
4 =4s
T=3
3
Figure 1.26