Chapter 1 Physical Quantities and Units

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Chapter 1
In the quest to understand nature, scientists use
physical quantities to describe the world around
us.
Physical Quantities and Units Part 2 Length
Time
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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 Systematic Errors
State 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 minimised by method of differences
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measurement of length
length
Length is the measurement of something from one
end to the other end.

• has a SI unit of metre (m)
• other units include centimetres (cm), millimetres
  (mm) and kilometres (km)

One metre is the distance travelled by light in a
vacuum in 1/299792458 of a second. Q What is the
speed of light?
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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
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measurement of length
parallax error
The eye must be positioned perpendicularly at the
mark on the scale to avoid parallax error.
8.3 cm correct
8.2 cm wrong
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

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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.
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measurement of length
engineers calipers
A pair of engineers 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.
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measurement of length
vernier calipers
Vernier calipers measure small lengths accurately
up to 0.01 cm.
inside jaws
tail
main scale
vernier scale
outside jaws
accuracy 0.1 mm / 0.01 cm
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measurement of length
vernier calipers
A
B
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
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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.
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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
1
main scale (fixed)
vernier scale (movable)
5
0
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
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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.
0
1
main scale (fixed)
vernier scale (movable)
5
0
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
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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
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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
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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.
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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.
supposing observed reading is 2.37 mm, then
corrected reading observed reading zero
error 2.37 (0.02)
2.35 mm
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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
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measurement of time
time

• has a SI unit of second (s)
• other units include years, months, days, hours,
  minutes and seconds

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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.
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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

B
A
O
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measurement of time
pendulum clock

• clocks make use of a process which is a regularly
  repeating motion (oscillations), such as the
  swing of a pendulum
• such oscillations are very regular so period is
  regular
• most modern clocks depend on the vibration of
  quartz crystals to keep time accurately
• in clocks that are wound up, elastic potential
  energy is stored in coiled springs

pendulum clock (cuckoo clock)
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measurement of time
watch

• used for measuring long intervals of time
• most modern watches depend on the vibration of
  quartz crystals to keep time accurately
• the energy that keeps these crystals vibrating
  comes from a small battery
• many watches still make use of coiled springs to
  supply the needed energy

wrist watch
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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.
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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.
steel strip
carbon paper disc
6 12 V a.c.
magnet
coil
ticker-tape
drawing pin
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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
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Physical quantities
are made up of
may be
include
Numerical values and suitable units
Vector Scalar
Base quantities Base SI units
use
such as
for
length (m) mass (kg) time(s) electric current
(A) temperature (K) amount of substance
(mol) luminous intensity (cd)
Prefixes
Measurement
e.g.
e.g. of
micro (?) 10-6 milli (m) 10-3 centi (c)
10-2 deci (d) 10-1 kilo (k) 103 mega (M) 106
Time
Length
can be measured with
can be measured with
metre rule half-metre rule measuring tape vernier
calipers micrometer screw gauge
pendulum clock watch stopwatch ticker-tape timer