1-PHYSICAL QUANTITIES, UNITS & MEASUREMENT131029195248-phpapp01.ppt

Unit and Measure
1
SCALARS AND VECTORS, MEASUREMENT TECHNIQUES, UNITS AND SYMBOLS
PHYSICAL QUANTITIES,
UNITS & MEASUREMENT

Unit and Measure 2
SCALARS AND VECTORS
DEFINE THE TERMS SCALAR AND VECTOR.

PHYSICAL DESCRIPTION
Unit and Measure 3
PHYSICAL
QUANTITY
VECTOR
QUANTITY
SCALAR
QUANTITY
A physical quantity is one that can be measured and that
consists of numerical magnitude and unit.

Unit and Measure 4
SCALAR
QUANTITY
Magnitude NO Direction

Unit and Measure 5
VECTOR
QUANTITY
Magnitude Direction

Unit and Measure 6
SCALARS AND VECTORS
L I S T T H E V E C T O R S A N D S C A L A R S F R O M D I S TA N C E , D I S P L A C E M E N T,
L E N G T H , S P E E D , V E L O C I T Y, T I M E , A C C E L E R AT I O N , M A S S A N D
F O R C E .

EXAMPLE OF SCALAR
Unit and Measure 7
distance
speed
time
mass
pressure energy
volume
density
power

EXAMPLE OF VECTOR
Unit and Measure 8
velocity
displacement
weight
acceleration
force

1. Which statement about scalars and vectors is correct?
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.
Unit and Measure 9

2. Which of the following correctly lists one scalar and one
vector quantity?
Unit and Measure 10
B

3. Which of the following groups of physical quantities
consists only of scalars?
A. acceleration, force, velocity
B. acceleration, mass, speed
C. force, time, velocity
D. mass, speed, time
Unit and Measure 11

4. Which list contains only scalar quantities?
A. acceleration, displacement, mass
B. acceleration, distance, speed
C. displacement, mass, velocity
D. distance, mass, speed
Unit and Measure 12

5. Which is the correct statement about force and
velocity?
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.
Unit and Measure 13

6. Which list contains only scalar quantities?
A. acceleration, displacement, velocity
B. distance, force, speed
C. force, length, time
D. length, mass, speed
Unit and Measure 14

7. A student studies some equations.
power = work / time
force = mass × acceleration
velocity = displacement / time
1. How many vector quantities are contained in the
equations?
Unit and Measure 15
A 1 B 2 C 3 D 4
D

8. The following statements are about motion.
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.
1. Which statements describe vector quantities?
A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 2 and 4
Unit and Measure 16

Unit and Measure 17
SCALARS AND VECTORS
DETERMINE THE RESULTANT OF TWO VECTORS BY A
GRAPHICAL MET HOD.

ADDING VECTOR
• In adding two vectors we need to consider the direction
of the vector quantities.
Unit and Measure 18
(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

VECTOR DIAGRAM
Unit and Measure 19

PARALLELOGRAM METHOD
Unit and Measure 20

WORKED EXAMPLE
Find the resultant force acting on the rocket shown below.
State the direction of this resultant force.
Unit and Measure 21
4 N
3 N

1. Set the scale of your drawing
• 1 cm to represent 1 N
2. Draw your two labelled vectors
Unit and Measure 22
4 N
3 N

3. Complete your rectangle
4. Draw your resultant vector
Unit and Measure 23
4 N
3 N

5. Measure your resultant vector and the direction
Unit and Measure 24
4 N
3 N

EXAMPLE
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.
Unit and Measure 25

3. An aircraft can fly at a top speed of 600 km/h.
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.)
Unit and Measure 26

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
a) the angle stream at which the boat must be pointed,
b) the resulting speed of the boat in the cross-stream direction.
Unit and Measure 27

5. By using a geometrical instrument, find the
resulting vector for each of the following;
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.
Unit and Measure 28

1. Two forces act at right angles at a point O as shown.
1. What is the resultant of the forces?
Unit and Measure 29
A

2. Which diagram correctly shows the addition of a 4 N and
a 3 N force?
Unit and Measure 30
A

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?
Unit and Measure 31
B

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

5. Two forces F1 and F2 act on an object O in the
directions shown.
Unit and Measure 34

1. What is the direction of the resultant force?
Unit and Measure 35
D

Unit and Measure 36
MEASUREMENT
TECHNIQUES
DESCRIBE HOW TO MEASURE A VARIETY OF LENGT H
WIT H APPROPRITATE ACCURACY USING TAPES, RULES,
MICORMETERS AND CALIPERS

39
Unit and Measure
F R O M 1 8 8 9 T O 1 9 6 0 , T H E M E T E R W A S D E F I N E D T O B E T H E D I S TA N C E
B E T W E E N T W O S C R AT C H E S I N A P L AT I N U M - I R I D I U M B A R .
PLATINUM-IRIDIUM BAR

40
Unit and Measure
T H E M E T R E I S D E F I N E D S U C H T H AT T H E S P E E D O F L I G H T I N F R E E
S PA C E I S E X A C T LY 2 9 9 , 7 9 2 , 4 5 8 M E T R E S P E R S E C O N D ( M / S )
ORANGE-RED LINE OF KRYPTON-86 PROPAGATING IN A
VACUUM

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

MEASUREMENT OF LENGTH
• 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
Unit and Measure 42

• 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

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

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

3. The diagram shows one method of measuring the
diameter of a beaker.
What is the diameter of the beaker?
Unit and Measure 46

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

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

6. A ruler is used to measure the length of a nail.
What is the length of the nail?
Unit and Measure 49

VERNIER CALIPER
Unit and Measure 50
Measure thickness or diameter of object correct to 2 decimal
places of decimals of a centimetre

• 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

EXAMPLE
Write down the reading shown by the following
Unit and Measure 56
(a) (c)
(b) (d)
0 5 10
7 8
0 5 10
6 7
0 5 10
0 1

barrel
thimble
circular
scale
main
scale
spindle
anvil
57
Unit and Measure
Measure diameter of wire or thin rod correct to 3 decimal places of centimetre
MICROMETER SCREWGAUGE
rachet head

• 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
Unit and Measure 58
mm
01
.
0
50
mm
50
.
0


• 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

EXAMPLE
1. Write down the reading shown by the micrometer screw
gauge.
Unit and Measure 64
(a) (c)
(b) (d)
25
30
0 5
40
5 10 15
45
5
10
0
30
35
0 5

2. Determine the reading of the following micrometer
screw gauge
Unit and Measure 65
(a)
(b)
0 5
15
20

RANGE & PRECISION
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
Unit and Measure 66

REVISION 1
Unit and Measure 67

REVISION 2
Unit and Measure 68

REVISION 3
Unit and Measure 69

REVISION 4
Unit and Measure 70

Unit and Measure 71
MEASUREMENT
TECHNIQUES
DESCRIBE HOW TO MEASURE A VARIETY OF T IME
INT ERVALS USING CLOCK AND STOPWATCHES

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

74
Unit and Measure
T H I S C L O C K D E P E N D S O N T H E O S C I L L A T I O N O F C A E S I U M - 1 3 3 A T O M .
T H E A C C U R A C Y I S T O 1 S E C O N D L O S S O R G A I N I N E V E R Y 2 0 M I L L I O N S Y E A R .
CAESIUM ATOMIC CLOCK

STOPWATCH
• 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)
Unit and Measure 75

PRECISION
Measuring
Instrument
Smallest
Division
Precisi
on
Examples
Analogue
stopwatch
0.1 s 0.1 s 25.1 s, 25.2 s, 25.3 s
Digital
stopwatch
0.1 s 0.1 s 25.1 s, 25.2 s, 25.3 s
0.01 s 0.01 s 25.12 s, 26.13 s, 26.14 s
Unit and Measure 76

1. A metre rule is used to measure a length.
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
Unit and Measure 77

2. In an experiment, a ball is rolled down a curved track
that is about half a metre long.
Unit and Measure 78

1. Which measuring device should be used to measure
the length accurately?
A. metre rule
B. micrometer
C. tape measure
D. vernier calipers
Unit and Measure 79

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

4. The diagram shows part of a vernier scale.
Unit and Measure 81
What is the correct
reading?
A. 30.5 mm
B. 33.5 mm
C. 38.0 mm
D. 42.5 mm

5. The width of a wooden block is measured using vernier
calipers.
Unit and Measure 82

1. What is the width of the block?
A. 3.5 mm
B. 5.3 mm
C. 8.0 mm
D. 8.5 mm
Unit and Measure 83

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

7. Vernier calipers read to one tenth of a millimetre.
8. Which reading shows this precision?
A. 3.3 cm
B. 3.31 cm
C. 3.310 cm
D. 3.312 cm
Unit and Measure 85

8. Vernier calipers are shown with the jaws closed.
Unit and Measure 86

1. What is the zero error?
A. 0.04 cm
B. 0.05 cm
C. 0.14 cm
D. 0.15 cm
Unit and Measure 87

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

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

11. Which instrument is used to measure the internal
diameter of a pipe with a single measurement?
A. manometer
B. measuring cylinder
C. micrometer
D. vernier calipers
Unit and Measure 90

12. A student has been asked to determine, as accurately
as possible, the volume of a piece of wire.
13. The wire is about 80 cm long and about 0.2 cm in
diameter.
Unit and Measure 91

1. Which measuring instruments should the student use?
Unit and Measure 92
A

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

1. Which instruments measure each of these dimensions
accurately?
Unit and Measure 94
A

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.
Unit and Measure 95

1. How long does the second athlete take to run 100 m?
A. 11.2 s
B. 11.4 s
C. 12.4 s
D. 23.8 s
Unit and Measure 96

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

1. Which statement about the time of the race is correct?
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.
Unit and Measure 98

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

1. How long did the car take to reach the observer?
A. 1.06 seconds
B. 6 seconds
C. 66 seconds
D. 106 seconds
Unit and Measure 100

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.

1. What is the time taken for the runner to run the second
lap?
A. 0 min 50 s
B. 1 min 10 s
C. 1 min 13 s
D. 2 min 03 s

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

19. One oscillation of a swinging pendulum occurs when
the bob moves from X to Y and back to X again.

1. Using a stopwatch, which would be the most accurate
way to measure the time for one oscillation of the
pendulum?
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.

20. A pendulum is set in motion and 20 complete swings
are timed. The time measured is 30 s.
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

UNITS AND SYMBOLS
R E C O G N I S E A N D U S E T H E C O N V E N T I O N S A N D S Y M B O L S C O N T A I N E D I N ‘ S I G N ,
S Y M B O L S A N D S Y S T E M A T I C S ’ , A S S O C I A T I O N O F S C I E N C E E D U C A T I O N , 2 0 0 0 .

QUANTITES, SYMBOL UNIT
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

QUANTITES, SYMBOL UNIT
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 

SOME PREFIXES OF SI UNITS
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

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