chap 1 - physical quantities, units and measurement

• physical quantity

  • can be measured
  • consisted of a numerical magnitude and a unit
  • eg: a height of 4.5m
• basic quantity + SI units + symbol for SI units

  • length -> metre, m
  • mass -> kilogram, kg
  • time -> second, s
  • electric current -> ampere, A
  • thermodynamic temperature -> kelvin, K
  • amount of substance -> mole, mol
• speed

  • distance travelled per unit time
  • SI unit = m/s

  base quantities

  • length and time

  derived quantity

  • speed
• prefixes for SI units

  • multiples

  > tera-, T = 10¹²

  > giga-,G =10⁹

  > mega-, M = 10⁶

  > kilo-,k = 10³

  • sub-multiples

  > deci-, d = 10⁻¹

  > centi-,c = 10⁻²

  > milli-,m = 10⁻³

  > micro-, u = 10⁻⁶

  > nano-,n = 10⁻⁹
• measurement of length

  • SI unit = meter (m)
  • instruments used ot measure length = meter ruler, measuring tape, digital calipers and digital micrometer screw-gauge
• metre ruler and measuring tape

  • metre ruler can measure lengths of up to one meter
  • measuring tape can measure lenghts of up to several meters and measure straight distance or curved surfaces
• avoiding errors of measurement

  • when using metre ruler, our eyes must be positioned such that our line of sight is perpendicular to the ruler to avoid parallax errors
  • avoid using the zero mark of the metre ruler as a start point to take measurements cuz wear and tear may make it unsuitable for measuring purposes
  • random errors are unpredictable and cluster around a mean value, which can be minimized by taking several reading and calculating the average
  • systematic errors are constant and predictable & can be avoided by calibrating the equipment
• digital calipers

  • used to measure the internal and external diameters of an object accurately
  • the tail -> measure the depth of an object
  • inside jaws -> measure the internal diameter of an object
  • outside jaw -> measure external diameter or width of an object
  • locking screw -> ensure that the jaws do not move apart
  • digital display -> show the numerical value
  • zero button -> rest the displayed length back to zero
• digital micrometer screw gauge

  • used to measure object that are too small to be measured using the digital calipers
  • anvil and spindle -> measure diameter of an object
  • ratchet -> can be turned to adjust the spindle so that the spindle is in contact with the object
  • digital display -> show numerical value
  • zero button -> reset the displayed length back to zero
• precision of an instrument

  • the smallest unit an instrument can measure
  • measuring tape -> 0 to several metres -> 0.1cm or 1mm -> eg: person´s waist
  • metre ruler ->0 to one metre -> 0.1cm or 1mm -> eg: height of a table
  • digital caliper-> 0 to 15cm -> 0.01cm or 0.01mm -> diameter of a test tube
  • digital micrometer screw gauge -> 0-2.5cm -> 0.0001cm or 0.001mm -> diameter of a wire
• measurement of time

  • SI unit : second (s)
  • measuring instrument -> stopwatch, clocks and pendulums

  -> depend on the accuracy and precision needed
• simple pendulum

  • a complete oscillations is the motion of a pendulum when it starts swinging from its starting point and ends it swings at its original starting point
  • the period of a simple pendulum is the time taken for one complete oscillation + depends on gravitational field strength and length of pendulum & independent of the mass of pendulum bob
• human reaction time (HRT)

  • most stopwatches can measure time to precision of 0.01s
  • as human reaction is about 0.3s-0.5s, which is a random error, the readings are usually recorded to 0.1s to account for this error
• scalar quantities

  • physical quantities that only have magnitude
  • distance, speed, mass, energy and time

  vector quantities

  • physical quantities that have both magnitude and direction
  • displacement, velocity, acceleration, force and weight
• distance

  • the total length covered by a moving object regardless of the direction of motion
  • its is a scalar quantity
  • the SI unit = metre (m)

  displacement

  • the distance measured in a straight line in a specific direction regardless of route taken
  • vector quantity
• speed

  • distance moved per unit time
  • scalar quantity
  • SI unit = metre per second (m/s)
  • formula = speed = distance / time

  velocity

  • rate of change of displacement
  • vector quantity
  • SI unit = metre per second (m/s)
  • formula = velocity = displacement / time taken