Chapter 1: Physical Quantities, Units and Measurements

PHYSICS Physical Quantities, Units and Measurements What Are Physical Quantities? All objects can be described by their physical quantities . A physical quantity is a quantity that can be measured . It typically consists of a numeral magnitude and a unit . E.g. 0.16 m. There are 7 basic physical quantities , or base quantities . We use a system of standardised units called SI units . Base quantities and their SI units Base Quantity SI Unit and Symbol Length Metre, m Mass Kilogram, kg Time Second, s Electric current Ampere, A (Thermodynamic) temperature Kelvin, K Amount of substance Mole, mol For physical quantities with very big or very small magnitudes, we can write them in the standard form with the format: A × 10 n , where 1 ≤ A < 10, where n is an integer. NOTE: The number of s.f. in the standard form varies in questions! Example of standard forms Example of Physical Quantity Magnitude and Unit Standard Form MADE BY 로켓 백만

PHYSICS Length of the F1 Singapore Grand Prix Circuit (hehe sanjay) 30 900 m 3.09 × 10 5 m Speed of light in vacuum 300 000 000 m/s 3.0 × 10 8 m/s Diameter of a hydrogen atom 0.000 000 000 05 m 5.0 × 10 -11 m We can also use common prefixes to represent submultiples (smaller than 10) and multiples (bigger than 10) of 10 of the SI units. Some common prefixes and their symbols Factor Prefix Symbol Multiples 10 12 10 9 10 6 10 3 tera- giga- mega- kilo- T G M k Submultiples 10 -1 10 -2 10 -3 10 -6 10 -9 deci- centi- milli- micro- nano- d c m µ n MADE BY 로켓 백만

PHYSICS How Do We Measure Physical Quantities? The objects in our physical world are in a range of sizes as indicated by their orders of magnitude . - *Size of a typical atom = 1 × 10 -10 m. Its order of magnitude is -10 . - *Size of Earth = 6.378 × 10 6 m. Its order of magnitude is 6 . We can measure the physical quantity of length using various measuring instruments . - The measuring tape is commonly used to measure objects up to one metre . - The metre rule is commonly used to measure objects that are up to several centimetres to one metre . - The digital calipers (i.e. Vernier calipers) are a useful instrument to measure objects’ internal and external diameters and depths that are up to 15 cm . - The digital micrometer screw gauge is used to measure objects that are up to 2.5 cm . We choose the most suitable measuring instrument based on its precision and range . - Precision is the smallest value that an instrument can measure. - Range is the bracket of values that an instrument can measure. Some common measuring instruments Instrument Precision Range Example of Usage Measuring tape 0.1 cm or 1 mm Up to several metres Length of a room MADE BY 로켓 백만

PHYSICS Metre rule 0.1 cm or 1 mm Up to one metre Length of a book Digital calipers 0.001 cm or 0.01 mm (record data to 0.01 cm) Between 1 cm to 10 cm Diameter of a test tube Digital micrometer screw gauge 0.0001 cm or 0.001 mm (record data to 0.001 cm) Less than 1 cm Diameter of a wire Errors can occur during experiments. - Parallax errors are caused by the inaccurate positioning of the observer’s eyes while taking readings. To avoid parallax errors, the eye should be positioned directly above the markings . - Zero error is the non-zero reading when we expect a zero reading . For example, an end of a metre rule starts at 0.1 cm instead of 0 cm due to wear and tear. An accurate reading can be obtained by subtracting the zero error from the measured reading . We can measure the physical quantity of time using a stopwatch . The SI unit for time is second (s) . The year, month, day, hour, minute are other units for measuring time. The simple pendulum consists of a heavy object (bob) attached to a string. The bob swings back and forth , called an oscillation . The time taken for the pendulum to complete a full oscillation (from point A to B and back to A) is called its period . MADE BY 로켓 백만

PHYSICS We can use the stopwatch to measure the period T of the simple pendulum. a) Let the bob swing back and forth at a small angle. Start the stopwatch when the pendulum is at the highest point and it is momentarily stationary to reduce random error. b) Count the number of full oscillations. Stop the stopwatch when 20 full oscillations are complete. c) Divide the time taken by the number of oscillations to obtain the average time taken for each oscillation, or the period. Period T = 𝑡 20 20 NOTE: The period is not affected by the mass of the bob or the angle of the swing . It depends on the length of the string with g as a constant. Most stopwatches can measure time to a precision of 0.01s. Digital stopwatches usually show readings up to two decimal places . However, we usually take readings to the nearest one decimal place . This is because, unlike the electronic sensors used in data loggers , stopwatches need to be started and stopped by hand . This manual operation introduces a random error called human reaction time . Human reaction time is about 0.3 - 0.5s . A common error occurs when the bob of the pendulum moves in a circular path rather than back and forth . This is called a conical pendulum which has a different period from a simple pendulum . A conical pendulum traces the shape of a cone with an angle θ (about the string) and a radius r . What Are Scalars and Vectors? Scalar quantities are physical quantities that have only magnitude . MADE BY 로켓 백만

PHYSICS Vector quantities are physical quantities that have both magnitude and direction . Common scalar and vector quantities Scalar Vector distance displacement speed velocity/ acceleration mass weight energy force time weight power moment (momentum) work done - pressure - Differences between Distance and Displacement: 1. Distance - The total length covered by a moving object regardless of the direction of motion - A scalar quantity - SI unit: metre (m) 2. Displacement - The distance measured in a straight line in a specified direction - A vector quantity - SI unit: metre MADE BY 로켓 백만

PHYSICS Speed is the distance moved per unit time . Velocity is the rate of change of displacement . Both quantities have the same SI unit of metre per second (m/s) . You can think of velocity as speed with a direction . Formulae for speed and velocity: Speed = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 Velocity = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 When we talk about the velocity of an object, we have to state the speed of the object and the