Chapter 1 Physical Quantities Units and Measurement Learning

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 1 Physical Quantities Quantitative versus qualitative • • Most observation in physics are quantitative Descriptive observations (or qualitative) are usually imprecise Qualitative Observations How do you measure artistic beauty? THEME ONE: MEASUREMENT Quantitative Observations What can be measured with the instruments on an aeroplane?

Chapter 1 Physical Quantities, Units and Measurement 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 SI units are common today THEME ONE: 4. 5 m Vehicles Not Exceeding 1500 kg In Unladen Weight MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 1 Physical Quantities Are classified into two types: • • Base quantities Derived quantities Base quantity is like the brick – the basic building block of a house THEME ONE: MEASUREMENT Derived quantity is like the house that was build up from a collection of bricks (basic quantity)

Chapter 1 Physical Quantities, Units and Measurement 1. 2 SI Units • SI Units – International System of Units Base Quantities Name of Unit Symbol of Unit length metre m mass kilogram kg time second s electric current ampere A temperature kelvin K amount of substance mol luminous intensity candela cd THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 2 SI Units This Platinum Iridium cylinder is the standard kilogram. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 2 SI Units THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 2 SI Units • Example of derived quantity: area Defining equation: area = length × width In terms of units: Units of area = m × m = m 2 Defining equation: volume = length × width × height In terms of units: Units of volume = m × m = m 2 Defining equation: density = mass ÷ volume In terms of units: THEME ONE: MEASUREMENT Units of density = kg / m 3 = kg m− 3

Chapter 1 Physical Quantities, Units and Measurement 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 = THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 = THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 2 SI Units Derived Quantity Relation with Base and Derived Quantities area length × width volume length × width × height density mass volume speed distance time acceleration change in velocity time force mass × acceleration newton (N) pressure force area pascal (Pa) work force × distance joule (J) power work time watt (W) THEME ONE: MEASUREMENT Unit Special Name

Chapter 1 Physical Quantities, Units and Measurement 1. 3 Prefixes • Prefixes simplify the writing of very large or very small quantities THEME ONE: Prefix Abbreviation Power nano n 10− 9 micro 10− 6 milli m 10− 3 centi c 10− 2 deci d 10− 1 kilo k 103 mega M 106 giga G 109 MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 3 Prefixes • Alternative writing method • Using standard form • N × 10 n where 1 N < 10 and n is an integer This galaxy is about 2. 5 × 106 light years from the Earth. THEME ONE: MEASUREMENT The diameter of this atom is about 1 × 10− 10 m.

Chapter 1 Physical Quantities, Units and Measurement 1. A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit. 2. The physical quantities can be classified into base quantities and derived quantities. 3. There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity. 4. The SI units for length, mass and time are metre, kilogram and second respectively. 5. Prefixes are used to denote very big or very small numbers. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 4 Scalars and Vectors • Scalar quantities are quantities that have magnitude only. Two examples are shown below: Measuring Mass THEME ONE: MEASUREMENT Measuring Temperature

Chapter 1 Physical Quantities, Units and Measurement 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 6 kg 4 kg + = 10 kg THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 4 Scalars and Vectors • Vector quantities are quantities that have both magnitude and direction A Force Magnitude = 100 N Direction = Left THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 4 Scalars and Vectors • Examples of scalars and vectors Scalars Vectors distance displacement speed velocity mass weight time acceleration pressure force energy momentum volume density THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 4 Scalars and Vectors Adding Vectors using Graphical Method • Parallel vectors can be added arithmetically 4 N 6 N 2 N THEME ONE: MEASUREMENT 4 N 2 N 2 N

Chapter 1 Physical Quantities, Units and Measurement 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 5. 0 cm 20. 0 N Direction = right – 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 4 Scalars and Vectors B A A B B THEME ONE: MEASUREMENT A

Chapter 1 Physical Quantities, Units and Measurement 1. Scalar quantities are quantities that only have magnitudes 2. Vector quantities are quantities that have both magnitude and direction 3. Parallel vectors can be added arithmetically 4. Non-parallel vectors are added by graphical means using the parallelogram law THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 5 Measurement of Length and Time • Table 1. 6 shows the range and precision of some measuring instruments Instrument Range of measurement Accuracy Measuring tape 0− 5 m 0. 1 cm Metre rule 0− 1 m 0. 1 cm Vernier calipers 0 − 15 cm 0. 01 cm Micrometer screw gauge 0 − 2. 5 cm 0. 01 mm THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 5 Measurement of Length and 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 5 Measurement of Length and Time Caesium atomic clock • 1999 - NIST-F 1 begins operation with an uncertainty of 1. 7 × 10− 15, or accuracy to about one second in 20 million years THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. 5 Measurement of Length and 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 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. THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 1. The metre rule and half-metre rule are used to measure lengths accurately to 0. 1 cm. 2. Vernier calipers are used to measure lengths to a precision of 0. 01 cm. 3. Micrometer are used to measure length to a precision of 0. 01 mm. 4. 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 THEME ONE: MEASUREMENT

Chapter 1 Physical Quantities, Units and Measurement 5. Zero error is due to instruments that do not read exactly zero when there is nothing being measured. 6. The time for one complete swing of a pendulum is called its period of oscillation. 7. As the length of the pendulum increases, the period of oscillation increases as well. THEME ONE: MEASUREMENT

Chapter 1 THEME ONE: Physical Quantities, Units and Measurement MEASUREMENT

Chapter 1 THEME ONE: Physical Quantities, Units and Measurement MEASUREMENT

Chapter 1 THEME ONE: Physical Quantities, Units and Measurement MEASUREMENT