6. SCALARS AND VECTORS
LIST THE VECTORS AND SCALARS FROM DISTANCE, DISPLACEMENT, LENGTH, SPEED, VELOCITY,
TIME, ACCELERATION, MASS AND FORCE.
Unit and Measure 6
9. 1. Which statement about scalars and vectors is
correct?
Unit and Measure 9
A. A scalar has direction but no size.
B. A scalar has size but no direction.
C. A vector has direction but no size.
D. A vector has size but no direction.
10. 2. Which of the following correctly lists one scalar
and one vector quantity?
B
Unit and Measure 10
11. 3. Which of the following groups of physical
quantities consists only of scalars?
Unit and Measure 11
A. acceleration, force, velocity
B. acceleration, mass, speed
C. force, time, velocity
D. mass, speed, time
12. 4. Which list contains only scalar quantities?
Unit and Measure 12
A. acceleration, displacement, mass
B. acceleration, distance, speed
C. displacement, mass, velocity
D. distance, mass, speed
13. 5. Which is the correct statement about force and
velocity?
Unit and Measure 13
A. Force and velocity are both scalars.
B. Force and velocity are both vectors.
C. Force is a scalar, velocity is a vector.
D. Force is a vector, velocity is a scalar.
14. 6. Which list contains only scalar quantities?
Unit and Measure 14
A. acceleration, displacement, velocity
B. distance, force, speed
C. force, length, time
D. length, mass, speed
15. Unit and Measure 15
7. A student studies some
equations. power = work / time
force = mass × acceleration
velocity = displacement / time
How many vector quantities are contained in the
equations?
A 1 B 2 C 3 D 4
D
16. 8. The following statements are about motion.
Unit and Measure 16
1. 1 A plane flies due East for 600 km.
2. A runner’s average speed in a race around a track is 5 m/s.
3. A snail crawls at 3 mm/s in a straight line towards a lettuce.
4. A tourist travels 500 km on a journey.
9. Which statements describe vector quantities?
1. 1 and 2
2. 1 and 3
3. 2 and 3
4. 2 and 4
18. ADDING VECTOR
• In adding two vectors we need to consider
the direction of the vector quantities.
(a)
(b)
(c)
(d)
(e)
30 N 50 N
4 m 8 m
500 N 800 N
73 m 26 m
6 m/s 6 m/s
Unit and Measure 18
21. WORKED EXAMPLE
Find the resultant force acting on the rocket
shown below. State the direction of this resultant
force.
4 N
Unit and Measure 21
3 N
22. 1. Set the scale of your drawing
• 1 cm to represent 1 N
1. Draw your two labelled vectors
4 N
3 N
Unit and Measure 22
23. 4. Draw your resultant vector
3. Complete your rectangle
4 N
3 N
Unit and Measure 23
24. 5. Measure your resultant vector and the direction
4 N
3 N
Unit and Measure 24
25. EXAMPLE
Unit and Measure 25
1. You walk 7 m south and then 3 m west. What is
your displacement from your starting point?
2. A toy car is moving 12 m eastwards. A child then
pushes it 2.6 m northward. What is the resulting
displacement of the car.
26. 3. An aircraft can fly at a top
speed of 600 km/h.
Unit and Measure 26
a) What will its speed be if it flies into a head-
wind of 100 km/h? (A head-wind blows in the
opposite direction to the aircraft.)
b) The pilot directs the aircraft to fly due north at
600 km/h. A side-wind blows at 100 km/h
towards east. What will be the aircraft’s
resultant velocity? (Give both its speed and
direction.)
27. 4. A motorboat moved across a stream
that flows at 3.5 m/s. In still water the
boat can do 4.6 m/s. Find
Unit and Measure 27
a) the angle stream at which the boat must be pointed,
b) the resulting speed of the boat in the cross-stream
direction.
28. 5. By using a geometrical instrument, find
the resulting vector for each of the
following;
Unit and Measure 28
a) A displacement of 5 m and 7 m acting at
45° to one another.
b) A velocity of 6 m/s and 8 m/s acting at 60°
to one another.
c) A force of 5 N and 4 N acting at 90° to one
another
d) Two forces of 4 N and 6 N acting on a body
with an angle of 50° between them.
29. 1. Two forces act at right angles at a point O as
shown.
Unit and Measure 29
1. What is the resultant of the forces?
A
30. 2. Which diagram correctly shows the addition of a 4
N and a 3 N force?
A
Unit and Measure 30
31. 3. Forces X and Y act on a block in the directions
shown on the scale diagram.
1. In which direction is the resultant force acting?
B
Unit and Measure 31
32. 4. Forces of 3 N and 4 N are acting as shown in the
diagram.
1. Which diagram may be used to find the resultant R
of these two forces?
Unit and Measure 32
34. 5. Two forces F1and F2act on an object O in the
directions shown.
Unit and Measure 34
35. 1. What is the direction of the resultant force?
D
Unit and Measure 35
36. MEASUREMENT TECHNIQUES
DESCRIBE HOW TO MEASURE A VARIETY OF LENGTH WITH APPROPRITATE
ACCURACY USING TAPES, RULES, MICORMETERS AND CALIPERS
Unit and Measure
37. FROM 1889 TO 1960, THE METER WAS DEFINED TO BE THE DISTANCE BETWEEN TWO SCRATCHES IN A
PLATINUM-IRIDIUM BAR.
Unit and Measure
PLATINUM-IRIDIUM BAR
38. THE METRE IS DEFINED SUCH THAT THE SPEED OF LIGHT IN FREE SPACE IS EXACTLY 299,792,458 METRES
PER SECOND (M/S)
Unit and Measure
ORANGE-RED LINE OF KRYPTON-86 PROPAGATING IN A
VACUUM
39. THE METRE
• The metre or meter is a base unit of length in the
metric system used around the world for general
and scientific purposes.
Unit and Measure 41
40. MEASUREMENT OF LENGTH
Unit and Measure 42
• Metre rule is used to measure length of
object.
• Precaution to be taken when using a ruler:
Avoid parallax error – the position of eye must be
in line with the reading to be taken.
Avoid zeros errors and end errors – if the ends of
the ruler are worn-out, it is advisable that
measurements should start from the 1 cm mark of
the scale
41. • Any instrument that are out of adjustment or with
some minor fault is still accurate as long as the zero
error is added or subtracted form the reading
shown on the scale.
Unit and Measure 43
42. EXAMPLE
1. A girl uses a rule to measure the length of a metal
rod. Because the end of the rule is damaged, she
places one end of the rod at the 1 cm mark as
shown.
How long is the metal rod?
Unit and Measure 44
43. 2. A piece of cotton is measured between two points
on a ruler.
When the length of cotton is wound closely around
a pen, it goes round six times
What is the distance once round the pen?
Unit and Measure 45
44. 3. The diagram shows one method of measuring the
diameter of a beaker.
What is the diameter of the beaker?
Unit and Measure 46
45. 4. The diagram shows a thick-walled tube. The
thickness of the wall is 3 mm.
What is the internal diameter d of the tube?
Unit and Measure 47
46. 5. A floor is covered with square tiles. The diagram
shows a ruler on the tiles.
How long is one tile?
Unit and Measure 48
47. 6. A ruler is used to measure the length of a nail.
What is the length of the nail?
Unit and Measure 49
49. • The inside jaws which can be used to measure the internal
diameters of tube and containers.
• The depth bar at the end is used to measure the depth of a
container.
Unit and Measure 51
56. 50
Unit and Measure 58
• Micrometer screwgauge is used to measured the
diameter of fine wires, the thickness of paper and
similar small lengths.
• It has two scales: the main scale on the sleeve and
the circular scale on the thimble which have 50
divisions. One complete turn of the thimble moves
the spindle by 0.50 mm.
• Hence each divisions represents a distance of
0.50 mm
0.01mm
61. • There are number of precautions one should
take when using a micrometer:
• The thimble should never be tightened too much.
• Clean the ends of the anvil and spindle before making a
measurement.
• Check for systematic error by closing the micrometer when
there is nothing between its anvil and spindle.
Unit and Measure 63
62. EXAMPLE
1. Write down the reading shown by the micrometer
screw gauge.
(a) (c)
(b) (d)
25
30
0 5
40
5 10 15
45
5
10
0
30
35
0 5
Unit and Measure 64
63. 2. Determine the reading of the following micrometer
screw gauge
(a)
(b)
0 5
15
20
Unit and Measure 65
64. RANGE & PRECISION
Unit and Measure 66
Instrument
Range of
measurement
Precision
Measuring tape 0 – 5 m 0.1 cm
Metre rule 0 – 1 m 0.1 cm
Vernier calipers 0 – 15 cm 0.01 cm
Micrometer screw
gauge
0 – 2.5 cm 0.001 cm
71. TIME
• Time is measured in years, months, days, hours,
minutes & seconds.
• The second is the SI unit of time.
• All timing devices make use of some regular process
such as regularly repeating motions called
oscillations.
• One regular oscillations is referred to as the period of
the oscillation.
Unit and Measure 73
72. Unit and Measure
THIS CLOCK DEPENDS ON THE OSCILLATION OF CAESIUM-133 ATOM.
THE ACCURACY IS TO 1 SECOND LOSS OR GAIN IN EVERY 20 MILLIONS YEAR.
CAESIUM ATOMIC CLOCK
73. STOPWATCH
Unit and Measure 75
• Stopwatches are used to measure short intervals of
time.
• There are two types; the digital stopwatch and
analog watch.
• The digital stopwatch is more precise as it can
measure time intervals of 0.01 seconds while the
analogue stopwatch measures in intervals of 0.1
seconds.
• One common error in using stopwatches is the
reaction time in starting and stopping the watch
which is few hundredths of a second (typically 0.3 s)
75. 1. A metre rule is used to measure a length.
Unit and Measure 77
2. Which reading is shown to the nearest millimetre?
A. 0.7 m
B. 0.76 m
C. 0.761 m
D. 0.7614 m
76. 2. In an experiment, a ball is rolled
down a curved track that is about half a
metre long.
Unit and Measure 78
77. 1. Which
measuring
Unit and Measure 79
device should be used to
measure the length accurately?
A. metre rule
B. micrometer
C. tape measure
D. vernier calipers
78. 3. The diagram shows a vernier V placed against a
scale S.
1. What is the vernier reading?
A. 2.23
B. 2.26
C. 2.33
D. 2.36
Unit and Measure 80
79. 4. The diagram shows part of a vernier scale.
What is the correct
reading?
A.30.5 mm
B.33.5 mm
C.38.0 mm
D.42.5 mm
Unit and Measure 81
80. 5. The width of a wooden block is measured using
vernier calipers.
Unit and Measure 82
81. 1. What is the width of the block?
Unit and Measure 83
A. 3.5 mm
B. 5.3 mm
C. 8.0 mm
D. 8.5 mm
82. 6. The diagram shows a vernier scale.
1. What is the reading on the vernier scale?
A. 6.50 cm
B. 6.55 cm
C. 7.00 cm
D. 7.05 cm
Unit and Measure 84
83. 7. Vernier calipers read to one tenth of a millimetre.
Unit and Measure 85
8. Which reading shows this precision?
A. 3.3 cm
B. 3.31 cm
C. 3.310 cm
D. 3.312 cm
85. 1. What is the zero error?
Unit and Measure 87
A. 0.04 cm
B. 0.05 cm
C. 0.14 cm
D. 0.15 cm
86. 9. The diagram shows a micrometer scale.
1. Which reading is shown?
A. 5.64 mm
B. 7.14 mm
C. 7.16 mm
D. 7.64 mm
Unit and Measure 88
87. 10. What is the reading on this micrometer?
A. 5.43 mm
B. 6.63 mm
C. 7.30 mm
D. 8.13 mm
Unit and Measure 89
88. 11. Which instrument is used to measure the internal
diameter of a pipe with a single measurement?
Unit and Measure 90
A. manometer
B. measuring cylinder
C. micrometer
D. vernier calipers
89. 12. A student has been asked to determine, as
accurately as possible, the volume of a piece of
wire.
Unit and Measure 91
13. The wire is about 80 cm long and about 0.2 cm in
diameter.
90. 1. Which measuring instruments should the student
use?
A
Unit and Measure 92
91. 13. A manufacturer needs to measure accurately the
dimensions of a wooden floor tile.
14. The approximate dimensions of the tile are shown.
Unit and Measure 93
92. 1. Which instruments measure each of these
dimensions accurately?
A
Unit and Measure 94
93. 14. A stopwatch is used to time an athlete running
100
m. The timekeeper forgets to reset the watch to
zero before using it to time another athlete
running 100 m.
95
Unit and Measure
94. 1. How long does the second athlete take to run 100
m?
96
Unit and Measure
A. 11.2 s
B. 11.4 s
C. 12.4 s
D. 23.8 s
95. 15. Two digital stopwatches X and Y, which record in
minutes and seconds, are used to time a race.
16. The readings of the two stopwatches, at the start
and at the end of the race, are shown.
Unit and Measure 97
96. 1. Which statement about the time of the race is
correct?
Unit and Measure 98
A. Both stopwatches record the same time interval.
B. Stopwatch X recorded 10 s longer than stopwatch Y.
C. Stopwatch Y recorded 10 s longer than stopwatch X.
D. Stopwatch Y recorded 50 s longer than stopwatch X.
97. 16. The diagram shows a stopwatch, originally set at
00:00.
17. When a car was first seen, the stop-start button
was pressed. When the car passed the observer,
the stopwatch showed 01:06.
Unit and Measure 99
98. 1. How long did the car take to reach the observer?
Unit and Measure 100
A. 1.06 seconds
B. 6 seconds
C. 66 seconds
D. 106 seconds
99. 17. A student uses a stopwatch to time a runner
running around a circular track. The runner runs
two laps (twice around the track). The diagrams
show the reading on the stopwatch when the
runner starts running, at the end of the first lap,
and at the end of the second lap.
101
Unit and Measure
100. 1. What is the time taken for the runner to run the
second lap?
102
Unit and Measure
A. 0 min 50 s
B. 1 min 10 s
C. 1 min 13 s
D. 2 min 03 s
101. 18. Four athletes run twice around a track. The table
shows their times at the end of each lap.
19. Which athlete runs the second lap the
fastest?
D
103
Unit and Measure
102. 19. One oscillation of a swinging pendulum occurs
when the bob moves from X to Y and back to X
again.
Unit and Measure 104
103. 1. Using a stopwatch, which would be the most
accurate way to measure the time for one
oscillation of the pendulum?
Unit and Measure 105
A. Time 20 oscillations and multiply by 20.
B. Time 20 oscillations and divide by 20.
C. Time one oscillation.
D. Time the motion from X to Y, and double it.
104. 20. A pendulum is set in motion
and 20 complete swings are timed. The time
measured is 30 s.
Unit and Measure 106
21. What is the time for one complete swing of
the pendulum?
A. 0.67 s
B. 0.75 s
C. 1.5 s
D. 3.0 s
105. UNITS AND SYMBOLS
RECOGNISE AND USE THE CONVENTIONS AND SYMBOLS CONTAINED IN ‘SIGN, SYMBOLS AND SYSTEMATICS’,
ASSOCIATION OF SCIENCE EDUCATION, 2000.
Unit and Measure 107
106. QUANTITES, SYMBOL UNIT
Unit and Measure 108
Quantity Symbol Unit
length l km, m, cm, mm
mass m kg, g, mg
time t h, min, s, ms
temperature , T ᵒC
current I A, mA
107. QUANTITES, SYMBOL UNIT
Unit and Measure 109
Quantity Symbol Unit
volume V m3
, cm3
density g/cm3
, kg/m3
speed u, v km/h, m/s, cm/s
work done W
, E J, kWh
pressure p, P Pa, N/m2
current I mA, A
resistance R
108. SOME PREFIXES OF SI UNITS
Unit and Measure 110
Prefix Abbreviation Power Examples
micro 10-6
m, s
milli m 10-3
mm, mg
centi c 10-2
cm
kilo k 103 km, kg
mega M 106
MW, MB
