Theory of Measurements
Measurement of length and time
accurate measurement
No measurement is ever perfectly accurate. Even with high
precision instruments, some error is inevitable.
There are two main types of errors:
Random Errors
State
Systematic Errors
• random
• constant
Occurrence
• in all measurements
• observers estimate
the last figure of a
reading on an
instrument
• observers
consistently
underestimate or
overestimate a
reading
Remedy
• reduced by
averaging a large
number of readings
• minimized by
method of
differences
Measurement of length
length
Length is the measurement of something from
one end to the other end.
 has a SI unit of meter (m)
 other units include centimeters (cm),
millimeters (mm) and kilometers (km)
One meter is the distance travelled by light in a
vacuum in 1/299792458 of a second.
Measurement of length
length
Lengths can be measured by using the following:
 metre/half-metre rule
accuracy = 1 mm / 0.1 cm / 0.001 m
 measuring tape
accuracy = 1 mm / 0.1 cm / 0.001 m
Measurement of length
parallax error
The eye must be positioned perpendicularly at the mark on
the scale to avoid parallax error.
8.2 cm
wrong
8.3 cm
correct
8.5 cm
wrong
Parallax error is due to
 incorrect positioning of the eye
 the object is not at the same level as the markings of the
scale
Measurement of length
Zero error
Many instruments do not read zero exactly when
there is nothing being measured.
Reasons include:
 instruments are out of adjustment
 some minor fault is present in the instrument
Instruments are usually still accurate as long as
the zero error is added or subtracted from the
reading shown on the scale.
Measurement of length
Engineer’s calipers
A pair of engineer’s calipers and ruler are used for measuring
the lengths of objects without any flat sides.
the jaws are closed until
the points just touch the
object to be measured
remove the calipers and
measure the distance between
the jaws with a ruler.
Measurement of length
Vernier calipers
Vernier calipers measure small lengths accurately up to
0.01 cm.
inside jaws
tail
vernier scale
main scale
outside jaws
Accuracy = 0.1 mm / 0.01 cm
Measurement of length
vernier calipers
AB
C
main scale
(fixed)
vernier scale
(movable)
object being
measured
9 mm
reading on main scale (between A and B) = 2.4 cm
reading on vernier scale (C) = 0.08 cm
actual reading of object = 2.4 + 0.08
= 2.48 cm
Measurement of length
Vernier calipers
When the two jaws of the vernier calipers touch each other,
both zero marks on the main scale and on the vernier scale
should coincide.
If not, there is a zero error in the vernier calipers.
Measurement of length
Vernier calipers
If the two jaws touch each other, but the zero marks of the
main scale and vernier scale do not coincide as shown
below, the zero error is positive.
0
main scale
(fixed)
vernier scale
(movable)
0
1
5
10
zero error = +0.01 cm
supposing observed reading is 3.24 cm, then
corrected reading = observed reading – zero error
= 3.24 – (+0.01)
= 3.23 cm
Measurement of length
Vernier calipers
If the two jaws touch each other, but the zero marks of the
main scale and vernier scale do not coincide as shown
below, the zero error is negative.
main scale
(fixed)
vernier scale
(movable)
0
0
1
5
10
zero error = -0.02 cm
supposing observed reading is 4.03 cm, then
corrected reading = observed reading – zero error
= 4.03 – (-0.02)
= 4.05 cm
Measurement of length
Micrometer screw gauge
Micrometers measure small diameters or thicknesses.
anvil spindle sleeve
thimble
ratchet
frame
Accuracy = 0.01 mm / 0.001 cm
measurement of length
micrometer screw gauge
sleeve
thimble
reading on sleeve = 4.5 mm
reading on thimble = 0.12 mm
actual reading of object = 4.5 + 0.12
= 4.62 mm
Measurement of length
Micrometer screw gauge
When the anvil and spindle of the micrometer
touch each other, the scales should read zero.
If not, there is a zero error in the micrometer.
measurement of length
micrometer screw gauge
If the anvil and spindle touch each other, but the scales do
not read zero as shown below, the zero error is positive.
} 2 divisions
supposing observed reading is 2.37 mm, then
corrected reading
= observed reading – zero error
= 2.37 – (+0.02)
= 2.35 mm
Measurement of length
Micrometer screw gauge
If the anvil and spindle touch each other, but the scales do
not read zero as shown below, the zero error is negative.
} 3 divisions
supposing observed reading is 2.87 mm, then
corrected reading = observed reading – zero error
= 2.87 – (-0.03)
= 2.90 mm
Measurement of time
Time
 has a SI unit of second (s)
 other units include years, months, days, hours,
minutes and seconds
Measurement of time
Time
Time can be measured by using the following:
 clocks
 analogue
stopwatch
 digital
stopwatch
All timing devices make use of some regular process.
Measurement of time
The period of a simple pendulum
Time can also be measured
by using the following
simple pendulum.
pendulum bob
tied to one end
of a thread
 oscillations are regularly
repeating motions
 the period is time in
which 1 oscillation occurs
A
O
B
measurement of time
Stopwatch
A stopwatch is used to measure short intervals of time.
 stopwatches (analogue and digital)
accuracy = 0.1 s
accuracy = 0.01 s
When using a digital stopwatch to
time a race, the time to the nearest
0.1 s should be given.
Measurement of time
Ticker-tape timer
An electrical device that makes use of the oscillations of a
steel strip to mark short intervals of time.
6 ~ 12 V a.c.
coil
magnet
steel strip
ticker-tape
carbon paper disc
drawing pin
Measurement of time
Ticker-tape timer
 steel strip vibrates 50 times a second; therefore 50 dots
are made in a second on the paper tape
10-dot tape
between 2 consecutive dots, time interval = 1 s / 50 dots
= (1/50) s or 0.02 s
as there are 10 spaces on a piece of tape,
time taken for the tape to pass through the timer
= 10 x 0.02 s
= 0.20 s
Physical quantities
are made up of
may be
include
Vector
Scalar
Base quantities
Base SI units
Numerical values
and suitable units
such as
length (m)
mass (kg)
time(s)
electric current (A)
temperature (K)
amount of substance (mol)
luminous intensity (cd)
for
use
Measurement
Prefixes
e.g.
e.g. of
Length
can be measured with
metre rule
half-metre rule
measuring tape
vernier calipers
micrometer screw gauge
Time
micro ()
milli (m)
centi (c)
deci (d)
kilo (k)
mega (M)
can be measured with
pendulum clock
watch
stopwatch
ticker-tape timer
10-6
10-3
10-2
10-1
103
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