1 Chapter 1 Measurement

2 1.1 What is Physics? Physics is the study of Matter and Energy. This includes sub-topics like: General Physics Thermal Physics Light and Waves Electricity and Magnetism

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4 1.2 Physical Quantities and SI Units What is a Physical Quantity? A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit. 7 base quantities and 7 base SI units

5 1.2 Physical Quantities and SI Units All other physical quantities can be derived from these seven base quantities. These are called derived quantities.

6 1.2 Physical Quantities and SI Units Some common SI prefixes are listed in the table below. Alternatively, you can express the quantities in standard form.

7 1.2 Physical Quantities and SI Units Exercise 1 Rewrite the following measurements in the units suggested (a) 760 mm in m0.76 m (b) 3.2 ×10 3 m in km3.2 km (c) 4.5 µs in s4.5 ×10 -6 s (d) cm in mm1 mm (e) 7.2 km in mm7.2 ×10 6 mm (f) 2.5 ms in µs2.5 ×10 3 µs

8 1.2 Physical Quantities and SI Units Key Ideas A physical quantity has a numerical magnitude and a unit. The are seven base quantities: length, mass, time, electric current, temperature, luminous intensity and amount of substance. The units of these seven base quantities are known as the SI base units: m, kg, s, A, K, cd, mole

9 1.3 Measurement of Length The SI unit for length is the metre (m). Some of the common instruments that we used to measure lengths are the: Metre rule Tape measure Calipers Vernier calipers Micrometer screw gauge

Measurement of Length Metre rules and tape measures Metre rules can measure lengths up to 1 m. Tape measures can measure lengths up to a few metres.

Measurement of Length Precision of an Instrument The precision of an instrument is the smallest unit that the instrument can measure. What is the precision of the metre rule? The smallest unit the metre rule can measure is 0.1 cm or 1 mm. Hence, we say that the metre rule has a precision of 0.1 cm.

Measurement of Length Possible Errors I. Parallax Errors (Human) Due to the incorrect positioning of the eye when taking a measurement. Example: reading of a clock or speedometer, using metre rule to measure the length of an object.

Measurement of Length I. Parallax Errors (Human) How to avoid parallax errors? When using the metre rule, position your eye directly above the markings to avoid parallax errors. By taking several readings and taking the average, you will minimize reading errors.

Measurement of Length Calipers For measuring the diameters of cylinders or circular objects.

Measurement of Length Vernier Calipers For measuring both internal and external diameters of objects. It consists of a main scale and a sliding vernier scale. It has a precision of 0.01 cm.

Measurement of Length Guide to using the vernier calipers

Measurement of Length Possible Errors II. Zero Errors (Machine + Human) Zero mark on the main scale does not coincide with the zero mark on the vernier scale when not measuring anything between the jaws. Before using the vernier calipers, it is important to check the instrument for zero error.

Measurement of Length

Measurement of Length Exercise 2 State the reading of the vernier calipers in the figure below. Zero error = cm Observed reading = 3.24 cm Therefore, corrected reading = 3.24 – (+0.01) = 3.23 cm

20 Exercise 2 State the reading of the vernier calipers in the figure below. Zero error = – 0.02 cm Observed reading = 4.03 cm Therefore, corrected reading = 4.03 – ( – 0.02) = 4.05 cm 1.3 Measurement of Length

Measurement of Length Micrometer Screw Gauge It is used to measure the diameters of wires or ball bearings. It can measure to a precision of 0.01 mm.

Measurement of Length

23 Exercise 3 State the reading of the micrometer screw gauge in the figure below. Zero error = mm Observed reading = 2.37 mm Therefore, corrected reading = 2.37 – (+0.02) = 2.35 mm 1.3 Measurement of Length

24 Exercise 3 State the reading of the micrometer screw gauge in the figure below. Zero error = – 0.03 mm Observed reading = 3.86 mm Therefore, corrected reading = 3.86 – ( – 0.03) = 3.89 mm 1.3 Measurement of Length

25 Key Ideas Instruments with their range and precision. 1.3 Measurement of Length

26 Key Ideas Errors to take note for each instrument. 1.3 Measurement of Length

27 Test Yourself Figure 1.17 shows a voltmeter with a strip of mirror mounted under the needle and near the scale. Suggest how this may help to reduce errors when taking a reading. Answer: When taking a reading, ensure that your vision is placed directly above the needle so that the image of the needle coincides with the needle. This helps to reduce parallax error. Figure 1.17 Voltmeter scale with mirror mounted under the needle 1.3 Measurement of Length

28 2. Vernier calipers are used to measure the diameter of a ball bearing. What is the reading of the vernier scale? Answer: Step 1: Main scale reading: 2.5 cm Step 2: Vernier coincides with 3 rd line. Vernier scale reading is 0.03 cm. Step 3: Reading of diameter = cm = 2.53 cm 1.3 Measurement of Length

29 3. The diameter of a wire is measured using a micrometer screw gauge. A student takes an initial zero reading and then a reading of the diameter. What is the corrected diameter of the wire in mm? A 3.37 B 3.85 C 3.89 D 3.87 Answer: The zero reading Z = mm The diameter reading D = 3.87 mm Hence the corrected diameter reading: D corrected = D – Z = 3.87 – (+0.02) = 3.85 mm Therefore the answer is B. 1.3 Measurement of Length

30 Using a pendulum to measure time A simple pendulum consists of a bob attached to a string. A complete to-and-fro motion from R to S and back to R is one complete oscillation. The period T is the time taken for one complete revolution. 1.4 Measurement of Time

31 Instruments for telling time All instruments use some kind of periodic motion to tell time e.g. mechanical watches or clocks use the oscillations of springs, quartz watches use the natural vibrations of crystals. Stopwatches can measure time to a precision of 0.1 s. Digital stopwatches can show readings to two decimal places of a second. However, human reaction time introduces an error of about 0.3–0.5 s. 1.4 Measurement of Time

32 Key Ideas Time intervals are measured by observing events that repeat themselves. Clocks can be used to measure time intervals in minutes or hours. Stopwatches can be used to measure time intervals to a precision of 0.1 s. The period T is the time taken for the pendulum to swing from one end to the other and back again to its starting position. 1.4 Measurement of Time

33 Key Ideas Time intervals are measured by observing events that repeat themselves. Clocks can be used to measure time intervals in minutes or hours. Stopwatches can be used to measure time intervals to a precision of 0.1 s. The period T is the time taken for the pendulum to swing from one end to the other and back again to its starting position. 1.4 Measurement of Time

Measurement of Time Test Yourself How can you determine the period of the swing in the playground? Answer: Start the swing in its to-and-fro motion. When the motion is steady, start the stopwatch when the swing is at one end of its motion. Stop the stopwatch after 20 oscillations. Record the time t 1. Repeat steps 2-3 for another set of reading t 2. Take average t = The period T is given by T = 2 (t 1 + t 2 ) 20 t

Measurement of Time 2. Figure 1.26 shows an oscillating pendulum. If the time taken for the pendulum to swing from A to C to B is 3 s, what is the period of the pendulum? Answer: Moving from A to C to B only covers three-quarters of the oscillation. Hence, s  3 T 3 s T 4 3 = = =

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