Physical Quantities, Units and Measurement Name: ________________ Class: _________________ Index: ________________

Physics is the study of the natural world around us – from the very large, such as the solar system, to the very small, such as the atom. The study of Physics is commonly divided into major topics such as General Physics, Thermal Physics, Light, Waves and Sound, Electricity and Magnetism. All these topics are related to two main ideas: Matter and Energy.

What is Physics?

A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit. There are altogether seven basic physical quantities. Base QuantityName of SI unitSymbol for SI unit Lengthmetrem Masskilogramkg Timeseconds Electric CurrentampereA Thermodynamic Temperature kelvinK Luminous Intensitycandelacd Amount of SubstancemoleMol

All other common physical quantities such as area, volume and speed are derived from these seven quantities. They are called derived quantities. For example, speed is derived from length (distance travelled) and time. Physical QuantityHow it is derived from base quantities Symbol for unit Arealength x widthm2m2 Volumelength x width x heightm3m3 Speedlength/timems -1

Prefixes for SI Units The use of prefixes will make it more convenient to express physical quantities that are either very big or very small.

Apparatus for Measuring Length. (a)Metre Rule – A metre rule is used to measure length. The smallest division on a meter rule is 1 mm (0.1 cm or m). We attribute an uncertainty of 0.1 cm in the measured length. In conducting experiments in the school laboratory, we frequently use other types of ruler such as the half-metre rule and the 30-cm plastic rule. Figure 1

AB CD E F Name of Side Length Expressed In mmcmm AB BC ED Table 1

Measurements in Table 1 are called raw data. They are obtained from a measuring instrument and consists of two parts: i.a numerical value, and ii.a unit. All raw data are expressed to a fixed number of decimal places in a specified unit. This usually represents the precision to which the instrument can supply. Therefore, the length obtained with a meter rule should be given consistently to: i.three decimal places in metres (m), or ii.one decimal place in centimetres (cm), or iii.to the nearest millimetre (mm). Length of wooden plank = m Numerical Value Unit Width of wooden plank = 9.8 cm

Figure 2 When using a metre rule, care must be taken to avoid parallax error (Figure 2). This arises when the eye is not positioned vertically above the mark to be measured. At the incorrect position marked I, the mark seems to correspond to the 5.1 cm line on the scale. When viewed vertically at C, it is 5.0 cm.

Figure 3 Check the ruler for end errors before making a measurement. This could arise when the end of the ruler is worn or the zero mark is not at the edge of the object (Figure 3).

Figure 4 To measure the extension of a loaded spring, a needle can be attached on the base of the load and its tip protruding onto a scale along the line of sight of the person taking the reading. A vertical plane mirror fixed behind the ruler can help to eliminate parallax error (Figure 4).

Figure 5 Set squares are used to align objects to the metre-rule scale to improve accuracy of reading. This is illustrated in Figure 5 where the diameter of the sphere can be obtained by subtracting R 2 with R 1.Measurements should be repeated by rotating the sphere.

(b) Vernier Calipers A vernier caliper is used to measure short lengths such as internal diameter of a test tube. The smallest length that the vernier caliper (Figure 6) can measure is 0.1 mm. We attribute an uncertainty of 0.1 mm to the measured length when we use a vernier caliper. Figure 6

When the jaws of the vernier caliper are closed, the zeros of the main scale and vernier scale should coincide. If it doesn’t, the discrepancy is known as zero-error (Figure 7) and has to be subtracted from the value obtained through measurement. The zero error is an example of systematic error that will cause the measured value to be either too large or too small when compared to the true value. Correct measurement = Actual measurement – zero error Figure 7

Treatment of zero error is shown in Figure 8. Figure 8

(c) Micrometer Screw Gauge A micrometer screw gauge is used to measure lengths of small objects such as the diameter of human hair with a precision better than that of the vernier calipers. Figure 9 shows an actual micrometer screw gauge. The smallest length that the micrometer can measure is 0.01 mm. This is the precision of the micrometer. The spindle will move 0.01 mm horizontally away from the anvil when the thimble moves vertically downwards by one small division. Figure 9

When the anvil and spindle are closed, the zero mark on the circular scale coincides with the horizontal line on the main scale. If it doesn’t, the discrepancy is known as zero-error (Figure 10) and has to be subtracted from the value obtained by measurement. Zero error is an example of a systematic error that will cause the measured value to be either too large or too small when compared to the true value. Correct measurement = Actual measurement – zero error Figure 10

Treatment of zero-error is shown in Figure 11. Figure 11

Table 2 Table 2 summarizes the precision of the metre rule, vernier calipers and the micrometer screw gauge.

Reading for X 1 Reading for X 2 Reading for X 3 Figure 12 To find the average diameter of a uniform rod (Figure 12), we take readings at several positions (at least 3). Average Diameter = (X 1 + X 2 + X 3 ) / 3

Techniques in measuring small quantities without using special instruments. 1)Thickness of 1 piece of paper - Use a metre rule to measure the thickness of 100 sheets of paper. - Thickness of 1 sheet of paper = Total Thickness / ) Diameter of a piece of wire - Wind the wire around a thin rod or a pencil to form a tight coil, say 18 turns (Figure 13). Use a metre rule to measure the length of the coil, d cm. - Diameter of the wire = d / 18 Figure 13

Orders of Magnitude

Apparatus for measuring volume and mass (a)Measuring cylinder The SI unit for the measurement of volume is m 3. As volumes measured in the laboratory are small, alternative units such as dm 3, cm 3 and mm 3 are used. The conversion factors are given below: 1cm 3 = 1 ml 1 dm 3 = 1000 cm 3 = 1 litre 1 m 3 = 1000 dm 3 Figure 14

The precision of some apparatus used to measure volume is summarized in Table 3. Table 3

When the volume of a small irregular solid is required, it could be lowered directly into a cylinder containing a known initial volume of water. The volume of the solid can be obtained by subtracting the final volume of water to the initial volume. If the solid is too large and irregular, the solid is immersed in a displacement can filled to the brim with water. The volume of water can be read directly from the measuring cylinder (Figure 15). Figure 15

(b) Measuring mass Mass is commonly measured by one of the following measuring instruments. 1)Spring Balance (or Newton-meter) Spring balance makes use of the force of gravity acting on an object to extend or compress a spring. It measures weight when an object is attached to the hook. Modern spring balances are calibrated in both kilogram and newton (Figure 16). Figure 16

2) Electronic Balance (or top pan balance) The mass to be measured is placed on a top pan. The force of gravity deforms a substance within the balance. This alters the resistance and the current flowing through. The variation of the current with mass is then calibrated in grams. See Figure 17. Figure 17

The SI unit used in the spring balance is the Newton (N). The unit displayed on the electronic balance is the gram (g). The precision of some commonly used electronic balances are summarized in Table 4. Table 4

(c) Techniques in measuring small volume and small mass 1)Volume of 1 ball bearing (i) Use a measuring cylinder which is partially filled with water. The volume of water in the measuring cylinder V 1 is read. 100 ball bearings are then placed inside the measuring cylinder and the new reading V 2 is taken. See Figure 18. (ii) The volume of each ball bearing = (V 2 – V 1 ) / 100 2) Mass of 1 sheet of paper (i) Use a balance to measure the mass of 100 sheets of paper. (ii) Mass of 1 sheet of paper = Total mass / 100 Figure 18

Using a pendulum to tell time A simple pendulum can be used to measure time more accurately. It consists of a heavy object called a bob, like a small ball, attached to a string. The string is fixed at one end. If we swing the pendulum, it will move back and forth at regular intervals. Each complete to-and-fro motion is one oscillation. The period of the simple pendulum is the time taken for one complete oscillation.

Apparatus for Measuring Time (a) Analogue and digital stopwatches Time can be measured with an analogue stopwatch or a digital stopwatch (Figure 19). The oscillations of natural vibrations of crystals are used in clocks and watches as they are small, accurate and require very little electrical energy. Analogue stopwatch Digital stopwatch Figure 19 The SI unit for time is the second (s).

The precision of commonly used analogue stopwatch and digital stopwatch are summarized in Table 4. Table 5

(b) Techniques in measuring time in oscillations A simple pendulum consists of a bob suspended from a fixed support by a string (Figure 20). One period of a simple pendulum is the time taken for a complete oscillation. The period increases as the length of the pendulum increases. Figure 20

Apparatus for measuring temperature (a)Liquid-in-glass thermometer An example of a liquid-in-glass thermometer is the mercury-in-glass thermometer. It has a range of -10°C to 110°C. The SI unit for temperature is the kelvin (K). The precision of the thermometer is summarized in Table 5. Table 6

(b) Techniques in measuring temperature When taking a reading, it is essential that the eye be at the same level as the mercury meniscus (Figure 21). This is to prevent parallax error. Figure 21 Figure 22 Temperature should be measured to half a degree (i.e. +/- 0.5°C). However an uncertainty of +/- 0.2°C could be obtained if a hand lens is used (Figure 22).

(c) Digital thermometer The digital thermometer shown in Figure 23 makes use of a thermocouple as its temperature sensor. Temperature within the range of -50°C to 1300°C can be read on the digital liquid crystal display. An accuracy of 0.1°C can be obtained from the instrument. Figure 23

Apparatus for measuring electrical quantities (1)Ammeter An ammeter is used to measure electric current. The SI unit for current is the ampere (A). An ammeter is always connected in series with other electrical components in the circuit (Figure 24). Before switching the circuit on, the ammeter should be checked for zero error. If the needle is not at zero graduation, the error can be eliminated by adjusting the screw at the needle pivot with a five cents coin or a screw driver. When taking the reading, the image of the needle in the mirror can be aligned with the needle to remove parallax error. Figure 24

(2) Voltmeter The voltmeter is an instrument that measures potential difference and its SI unit is the volt (V). The voltmeter is always connected in parallel across a resistor to determine the effective potential difference (Figure 25). In setting up an electrical circuit, it is advisable to connect all the components in series first. The voltmeter should be the last instrument to be connected. This is to reduce confusion and to prevent the voltmeter from being connected in series with resistances in the circuit. Figure 25

(3) Galvanometer The galvanometer is an electrical meter tat measures small current or the presence of a current. Its distinguishable feature is a small zero mark at the center of the scale (Figure 26). Figure 26

(4) Digital multimeter A digital multimeter is a versatile electronic instrument that can be used as an ammeter, voltmeter or an ohmmeter. By incorporating shunts, multipliers, variable resistors and an in-build battery, it is capable of measuring alternating current (a.c.), direct current (d.c.), voltages as well as resistances in an electric circuit (Figure 27). Figure 27

Precision of electrical instruments. Table 7

Apparatus and techniques in alignment (a)To ensure that a ruler is set up vertically Set up a plumb line and placed the ruler parallel to it. If the ruler appears to be parallel to the plumb line from the front and the side, the ruler must be vertical (Figure 28). Figure 28

(b) To ensure that a ruler is set up horizontally (1) Set up a plumb line and place the ruler perpendicular to the plumb line as shown in Figure 29. Use a set square to ensure that the angle between the plumb line and the ruler is 90°. Figure 29

(2) Place a spirit level on the meter rule and adjust the bubble to the centre of the spirit level (Figure 30). Figure 30

(3) Another method is to measure both ends of the meter rule from the top of the bench (Figure 31). Figure 31

(c) Measurement of angles The most common instrument used to measure angles is the protractor. Readings will be inaccurate if there is parallax error or poor alignment of the protractor. Figure 32 illustrates the incorrect and correct methods of alignment when measuring the angle Ɵ of the slope and is obtained by reading the outer scale of the protractor. Figure 32

References: Physics Insight “O” Level 2nd Edition. Loo Wan Yong, Loo Kwok Wai.