Learning outcomes

Understand that physical quantities have numerical magnitude and a unit Recall base quantities and use prefixes Show an understanding of orders of magnitude Understand scalar and vector quantities Determine resultant vector by graphical method Measure length with measuring instruments Measure short interval of time using stopwatches Learning outcomes

1.1 Physical Quantities Quantitative versus qualitative • Most observation in physics are quantitative • Descriptive observations (or qualitative) are usually imprecise Quantitative Observations What can be measured with the instruments on an aeroplane? Qualitative Observations How do you measure artistic beauty?

 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

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

SI Units – International System of Units 1.2 SI Units

1.2 SI Units This Platinum Iridium cylinder is the standard kilogram.

1.2 SI Units area volume speed density Word Splash Power acceleration force Work Pressure

1.2 SI Units • Example of derived quantity: area Defining equation: area = length × width In terms of units: Units of area = m × m = m2 Defining equation: volume = length × width × height In terms of units: Units of volume = m × m × m = m2 Defining equation: density = mass ÷ volume In terms of units: Units of density = kg / m3 = kg m−3

1.2 SI Units • Work out the derived quantities for: Defining equation: speed = In terms of units: Units of speed = Defining equation: acceleration = In terms of units: Units of acceleration = Defining equation: force = mass × acceleration In terms of units: Units of force =

1.2 SI Units • Work out the derived quantities for: Defining equation: Pressure = In terms of units: Units of pressure = Defining equation: Work = Force × Displacement In terms of units: Units of work = Defining equation: Power = In terms of units: Units of power =

1.2 SI Units

Prefixes simplify the writing of very large or very small quantities 1.3 Prefixes

1.3 Prefixes • Alternative writing method • Using standard form • N × 10n where 1 N< 10 and n is an integer The diameter of this atom is about 1 × 10−10 m. This galaxy is about 2.5 × 106 light years from the Earth.

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. • Prefixes are used to denote very big or very small numbers.

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

6 kg 4 kg 10 kg 1.4 Scalars and Vectors • Scalar quantities are added or subtracted by using simple arithmetic. • Example: 4 kg plus 6 kg gives the answer 10 kg + =

Arrgh A Force 1.4 Scalars and Vectors • Vector quantities are quantities that have both magnitude and direction Magnitude = 100 N Direction = Left

1.4 Scalars and Vectors • Examples of scalars and vectors

1.4 Scalars and Vectors • Adding Vectors using Graphical Method • Parallel vectors can be added arithmetically 4 N 6 N 4 N 2 N 2 N 2 N

1.4 Scalars and Vectors • Adding Vectors using Graphical Method • Non-parallel vectors are added by graphical means using the parallelogram law • Vectors can be represented graphically by arrows • The length of the arrow represents the magnitude of the vector • The direction of the arrow represents the direction of the vector • The magnitude and direction of the resultant vector can be found using an accurate scale drawing 20.0 N 5.0 cm Direction = right

1.4 Scalars and Vectors • The parallelogram law of vector addition states that if two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram

1.4 Scalars and Vectors • Another method of Adding Vectors • To add vectors A and B • place the starting point of B at the ending point of A • The vector sum or resultant R is the vector joining the starting point of vector A to the ending point of B • Conversely, R can also be obtained by placing the starting point of A at the ending point of B • Now the resultant is represented by the vector joining the starting point of B to the ending point of A • See next slide

1.4 Scalars and Vectors B A A B A B

Scalar quantities are quantities that only have magnitudes • Vector quantities are quantities that have both magnitude and direction • Parallel vectors can be added arithmetically • Non-parallel vectors are added by graphical means using the parallelogram law

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

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

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 are 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

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

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

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

1.5 Measurement of Length and Time • Table 1.6 shows the range and precision of some measuring instruments

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

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.

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

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.

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

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

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

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.

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

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.

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.

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

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.

1.5 Measurement of Length and Time • Errors occur in measuring time • If digital stopwatch is used to time a race, should not record time to the nearest 0.01 s. • reaction time in starting and stopping the watch will be more than a few hundredths of a second • an analogue stopwatch would be just as useful

1.5 Measurement of Length and Time • Ticker-tape Timer • electrical device making use of the oscillations of a steel strip to mark short intervals of time • steel strip vibrates 50 times a second and makes 50 dots a second on a paper tape being pulled past it • used only in certain physics experiments

1.5 Measurement of Length and Time • Ticker-tape Timer • Time interval between two consecutive dots is 0.02 s • If there are 10 spaces on a pieces of tape, time taken is 10 × 0.02 s = 0.20 s. • Counting of the dots starts from zero • A 10-dot tape is shown below.

The metre rule and half-metre rule are used to measure lengths accurately to 0.1 cm. • Vernier calipers are used to measure lengths to a precision of 0.01 cm. • Micrometer are used to measure length to a precision of 0.01 mm. • Parallax error is due to: • (a) incorrect positioning of the eye • (b) object not being at the same level as the marking on the scale

Zero error is due to instruments that do not read exactly zero when there is nothing being measured. The time for one complete swing of a pendulum is called its period of oscillation. As the length of the pendulum increases, the period of oscillation increases as well.

Learning outcomes