1.1 Physical Quantities

1.  4.5 m  1.1 Physical Quantities • A physical quantity is one that can be measured and consists of a magnitude and unit. Measuring length 70 km/h Vehicles Not Exceeding 1500 kg In Unladen Weight SI units are common today

2. 1.1 Physical Quantities Are classified into two types: • Base quantities • Derived quantities Derived quantity is like the house that was build up from a collection of bricks (basic quantity) Base quantity is like the brick – the basic building block of a house

3. SI Units – International System of Units 1.2 SI Units

4. A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit. • The physical quantities can be classified into base quantities and derived quantities. • There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity. • The SI units for length, mass and time are metre, kilogram and second respectively.

5. 1.4 Scalars and Vectors • Scalar quantities are quantities that have magnitude only. Two examples are shown below: Measuring Mass Measuring Temperature

6. 1.5 Measurement of Length and Time • Accurate Measurement • No measurement is perfectly accurate • Some error is inevitable even with high precision instruments • Two main types of errors • Random errors • Systematic errors

7. 1.5 Measurement of Length and Time • Accurate Measurement • Random errors occur in all measurements. • Arise when observers estimate the last figure of an instrument reading • Also contributed by background noise or mechanical vibrations in the laboratory. • Called random errors because they are unpredictable • Minimise such errors by averaging a large number of readings • Freak results discarded before averaging

8. 1.5 Measurement of Length and Time • Accurate Measurement • Systematic errors are not random but constant • Cause an experimenter to consistently underestimate or overestimate a reading • They Due to the equipment being used – e.g. a ruler with zero error • may be due to environmental factors – e.g. weather conditions on a particular day • Cannot be reduced by averaging, but they can be eliminated if the sources of the errors are known

9. 1.5 Measurement of Length and Time • Length • Measuring tape is used to measure relatively long lengths • For shorter length, a metre rule or a shorter rule will be more accurate

10. 1.5 Measurement of Length and Time • Correct way to read the scale on a ruler • Position eye perpendicularly at the mark on the scale to avoids parallax errors • Another reason for error: object not align or arranged parallel to the scale

11. 1.5 Measurement of Length and Time • Many instruments do not read exactly zero when nothing is being measured • Happen because they are out of adjustment or some minor fault in the instrument • Add or subtract the zero error from the reading shown on the scale to obtain accurate readings • Vernier calipers or micrometer screw gauge give more accurate measurements

12. 1.5 Measurement of Length and Time • Vernier Calipers • Allows measurements up to 0.01 cm • Consists of a 9 mm long scale divided into 10 divisions

13. 1.5 Measurement of Length and Time • Vernier Calipers • The object being measured is between 2.4 cm and 2.5 cm long. • The second decimal number is the marking on the vernier scale which coincides with a marking on the main scale.

14. 1.5 Measurement of Length and Time • Here the eighth marking on the vernier scale coincides with the marking at C on the main scale • Therefore the distance AB is 0.08 cm, i.e. the length of the object is 2.48 cm

15. 1.5 Measurement of Length and Time • The reading shown is 3.15 cm. • The instrument also has inside jaws for measuring internal diameters of tubes and containers. • The rod at the end is used to measure depth of containers.

16. 1.5 Measurement of Length and Time • Micrometer Screw Gauge • To measure diameter of fine wires, thickness of paper and small lengths, a micrometer screw gauge is used • The micrometer has two scales: • Main scale on the sleeve • Circular scale on the thimble • There are 50 divisions on the thimble • One complete turn of the thimble moves the spindle by 0.50 mm

17. 1.5 Measurement of Length and Time • Micrometer Screw Gauge • Two scales: main scale and circular scale • One complete turn moves the spindle by 0.50 mm. • Each division on the circular scale = 0.01 mm

18. 1.5 Measurement of Length and Time • Precautions when using a micrometer • 1. Never tighten thimble too much • Modern micrometers have a ratchet to avoid this • 2. Clean the ends of the anvil and spindle before making a measurement • Any dirt on either of surfaces could affect the reading • 3. Check for zero error by closing the micrometer when there is nothing between the anvil and spindle • The reading should be zero, but it is common to find a small zero error • Correct zero error by adjusting the final measurement

19. 1.5 Measurement of Length and Time • Time • Measured in years, months, days, hours, minutes and seconds • SI unit for time is the second (s). • Clocks use a process which depends on a regularly repeating motion termed oscillations.

20. Caesium atomic clock 1999 - NIST-F1 begins operation with an uncertainty of 1.7 × 10−15, or accuracy to about one second in 20 million years 1.5 Measurement of Length and Time

21. 1.5 Measurement of Length and Time • Time • The oscillation of a simple pendulum is an example of a regularly repeating motion. • The time for 1 complete oscillation is referred to as the period of the oscillation.

22. 1.5 Measurement of Length and Time • Pendulum Clock • Measures long intervals of time • Hours, minutes and seconds • Mass at the end of the chain attached to the clock is allowed to fall • Gravitational potential energy from descending mass is used to keep the pendulum swinging • In clocks that are wound up, this energy is stored in coiled springs as elastic potential energy.

23. 1.5 Measurement of Length and Time • Watch • also used to measure long intervals of time • most depend on the vibration of quartz crystals to keep accurate time • energy from a battery keeps quartz crystals vibrating • some watches also make use of coiled springs to supply the needed energy

24. 1.5 Measurement of Length and Time • Stopwatch • Measure short intervals of time • Two types: digital stopwatch, analogue stopwatch • Digital stopwatch more accurate as it can measure time in intervals of 0.01 seconds. • Analogue stopwatch measures time in intervals of 0.1 seconds.