1. Physical Quantities and Units
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 1

2. 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

3. 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/ of a second.
Q: What is the speed of light?

4. measurement of length length
Lengths can be measured by using the following:
metre/half-metre rule
accuracy = 1 mm / 0.1 cm / m
measuring tape
accuracy = 1 mm / 0.1 cm / m

5. 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

6. 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.

7. 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.

8. 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

9. vernier scale (movable)
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 =
= 2.48 cm

10. 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.

11. vernier scale (movable)
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. 1
main scale (fixed)
vernier scale (movable) 5 10
zero error = cm
supposing observed reading is 3.24 cm, then
corrected reading = observed reading – zero error
= 3.24 – (+0.01)
= 3.23 cm

12. vernier scale (movable)
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. 1
main scale (fixed)
vernier scale (movable) 5 10
zero error = cm
supposing observed reading is 4.03 cm, then
corrected reading = observed reading – zero error
= 4.03 – (-0.02)
= 4.05 cm

13. measurement of length micrometer screw gauge
Micrometers measure small diameters or thicknesses.
anvil
spindle
sleeve
thimble
ratchet
frame
accuracy = 0.01 mm / cm

14. measurement of length micrometer screw gauge
sleeve
thimble
reading on sleeve = 4.5 mm
reading on thimble = 0.12 mm
actual reading of object =
= 4.62 mm

15. 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.

16. 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

17. 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

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

19. 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.

20. pendulum bob tied to one end of a thread
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 B O

21. 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)

22. 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

23. 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.

24. 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.
steel strip
carbon paper disc
coil
magnet
ticker-tape
drawing pin

25. 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

26. Numerical values and suitable units Base quantities Base SI units
Physical quantities
are made up of
may be
include
Numerical values and suitable units
Base quantities
Base SI units
Vector
Scalar
such as
for
use
length (m)
mass (kg)
time(s)
electric current (A)
temperature (K)
amount of substance (mol)
luminous intensity (cd)
Measurement
Prefixes
e.g.
e.g. of
micro ()
milli (m)
centi (c)
deci (d)
kilo (k) 103
mega (M) 106
Length
Time
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