1. Measurements
By Mr Tan KK

2. Measuring Instruments
Rulers or measuring tapes
Avoid parallax errors – due to the wrong positioning of the eye or the object is not at the same level as the markings of the scale.
Correction: Eye must be positioned perpendicularly at the mark of the scale.

3. Measuring Instruments

4. Measuring Instruments
How about objects without any flat sides, e.g. sphere?
Can we use a ruler to make measurements?

5. Measuring Instruments
A pair of engineer’s calipers can be used which consist of a pair of steel jaws hinged at the base.
They are closed until the points just touch the object to be measured.
Then, when the calipers are removed, the distance between the jaws can be measured with a ruler.

6. Measuring Instruments
Metre Rule or measuring tape – accurate to 0.1 cm.
For greater precision, we need special instruments: vernier calipers and micrometre screw gauge.

7. Vernier Calipers
It consists of a scale of 9 mm divided into 10 divisions.

8. Vernier Calipers
In the figure, the object being measured has a length between 2.4 cm and 2.5 cm.
To find the second decimal number (given by the distance AB), we look for a marking on the vernier scale which coincides with a marking on the main scale.
In the Figure, the eighth marking on the vernier scale coincides with the marking at C on the main scale. This means that the distance AB is 0.08 cm, i.e., the length of the object is 2.48 cm.

9. Precautions
What are the 2 precautions that you should take when taking a reading from the vernier calipers?
Video on using the vernier calipers
Java Applet
Website: More Info on the Vernier Calipers

10. Using the Vernier Calipers
The reading shown is 3.15 cm. The instrument also has a pair of inside jaws which can be used to measure the internal diameters of tubes and containers. The scale is read in the same way. When the two jaws of the vernier calipers touch each other, both the zero marks on the main scale and on the vernier scale should coincide.
Otherwise there is a zero error in the vernier calipers

11. Correcting Zero Errors

12. Correcting Zero Errors

13. Micrometer Screw Gauge
For measuring the diameter of fine wires, the thickness of paper and similar small distances, a micrometer screw gauge (commonly shortened to micrometer) is used.
The micrometer has two scales: the main scale on the sleeve and the circular scale on the thimble.
One complete turn of the thimble moves the spindle by 0.50 mm. There are 50 divisions on the thimble. 0.50
Hence each division represents a distance of 50 mm = 0.01 mm.
A micrometer therefore allows us to measure accurately up to 0.01 mm.

14. Micrometer Screw Gauge

15. Precautions: Micrometer
The screw should never be tightened too much.
Some modern micrometers are fitted with a ratchet to avoid this, but in older models it is possible to damage the screw by overtightening.
Video
Applet on the usage of micrometer
Website: More Info on the micrometer

16. Precautions: Micrometer
It is a good experimental technique to clean the ends of the anvil and spindle before making a measurement.
Any dirt on either of these surfaces could affect the reading.
Lastly, check for systematic errors, e.g.?

17. Correcting Zero Errors
Zero error = _____________mm
Observed reading = __________ mm
Corrected reading = __________ mm

18. Correcting Zero Errors
Zero error = _____________mm
Observed reading = __________ mm
Corrected reading = __________ mm

19. Measuring Time
Time is measured in years, months, days, hours, minutes and seconds but the SI unit for time is the ________________.
All timing devices make use of some regular process.
Can you name some regular process?

20. Measuring Time
Most clocks use a process which is a regularly repeating motion, such as the swing of a pendulum.
Such repeating motions are termed oscillations.
The most accurate clock is the caesium clock (an atomic clock) which depends on the oscillation of a caesium-133 atom.

21. Measuring Time
This clock is accurate to a 1 second loss or gain in years.
Since such oscillations are very regular, the time in which one oscillation occurs should be constant.
This time is referred to as the period of the oscillation.

22. Measuring time
The pendulum clock is used to measure long intervals of time.
It measures time in hours, minutes and seconds.
The gravitational potential energy from the descending mass is used to keep the pendulum swinging.
How about clocks and watches?

23. Measuring Time
In clocks that are wound up, this energy is stored in coiled springs as elastic potential energy.
Watches are also used to measure long intervals of time.
Most modern watches and clocks depend on the vibration of quartz crystals to keep time accurately

24. Measuring Time
The energy to keep these crystals vibrating comes from a small battery.
However, there are still many watches making use of coiled springs to supply the needed energy.

25. Measuring Time
Stopwatches are used to measure short intervals of time.
There are two type of stopwatches: the digital stopwatch and the analogue stopwatch.
Which do you think is more accurate?

26. Measuring Time
The digital stopwatch is more accurate than the analogue stopwatch as can measure time in intervals of 0.01 seconds while the latter can only measure time in intervals of 0.1 seconds.

27. Measuring Time
Before giving the result of the time measurement, it is important to consider other errors involved.
For instance, if you use a digital stopwatch to time a race, you should not give the time to the nearest 0.01 s. Why?

28. Measuring Time
Before giving the result of the time measurement, it is important to consider other errors involved.
For instance, if you use a digital stopwatch to time a race, you should not give the time to the nearest 0.01 s. Why?

29. Measuring Time
The watch may be accurate, but your reaction time in starting and stopping the watch will be more than a few hundredths of a second typically 0.3 s.

30. Measuring Time
In this case, an analogue stopwatch would be just as useful.

31. Ticker Tape Timer
One timer used only in certain Physics experiments is the ticker-tape timer.
This is an electrical device making use of the oscillations of a steel strip to mark short intervals of time.
It consists of a steel strip which vibrates 50 times a second and makes 50 dots a second on a paper tape being pulled past it.

32. Ticker Tape Timer

33. Ticker Tape Timer
Between two consecutive dots there is a time interval of 1 50s or 0.02 s.
If there are 10 spaces on a piece of tape, what is the time taken for the tape to pass through?
10 x 0.02 s = 0.20 s.

34. Ticker Tape Timer
This section of the tape is also known as a 10-dot tape. Note that the counting starts from zero.

35. Reading Measuring Cylinder
Meniscus Reading