Physical quantities, units & measurements

• Length: The SI base unit is metre(m). Symbol: l

  Time: The SI base unit is second(s). Symbol: t

  Mass: The SI base unit is kilogram (kg). Symbol: m

  Electric current: The SI base unit is ampre(A) Symbol: I

  Temperature: The SI base unit is kelvin(K) Symbol: T

  Amount of Substance: The SI base unit is mole(mol). Symbol: n

  Luminous Intensity: The SI base unit is candela(cd). Symbol: Iv
• Physical quantities: a quantity that can be measured. Consists of a numerical magnitude and a unit. Divided into base and deprived.
• Deprived quantity:

  • Speed - $m/s , ms-1$
  • Density -$kg/m3$
  • Volume - m3
  • Area - m2
• Prefixes: used to represent very large numbers or very small quantities. Are placed before the units to indicate a multiple/fraction of the unit.
• • Giga(G) = 10^9 (1 000 000 000)
  • Mega(M) = 10^6 (1000 000)
  • Kilo(k) = 10^3 (1000)
  • Deci(d) = 10^-1 (0.1)
  • Centi(c) = 10^-2 (0.01)
  • Milli(m) = 10^-3 (0.001)
  • Micro(u) = 10^-6 (0.000 001)
  • Nano(n) = 10^-9 (0.000 000 001)
• Standard form: A way of writing numbers, in which a number between 1 to 10 is multiplied by an appropriate of 10.
• • A range of different instruments can be used to measure different lengths.
  • E.g. Measuring tape, metre rule, digital calipers & digital micrometer screw gauge
  • We need to choose the appropriate instrument when measuring a particular length.
• • Inside jaws - measures the internal diameter of an object
  • Outside jaws - measures the external diameter of an object
  • Locking screw - ensures that the jaws do not move apart
  • Tail - measures the depth of an object
  • Zero button - resets the displayed length back to zero
  • Digital display - shows the numeric value

  A) tail

  
• • Anvil & Spindle - measure the diameter of an object
  • Ratchet - can be turned to adjust the spindle so that the spindle is in contact with the object
  • Digital display - shows the numeric value
  • Zero button - resets displayed length back to zero

  
• Measuring length:

  • Metre rule - measures the length of up to 1 metre
  • Measuring tape (Steel) - measures straight distances longer than a metre.
  • Measuring tape (cloth)- measures the length along a curved surface.
• Precision: the smallest unit an instrument can measure.

  • Measuring tape - Several centimetres up to a few metres (0.1cm or 1mm)
  • Metre rule - Several centimetres up to a metre (0.1cm or 1mm)
  • Digital calipers - Typically 1cm to 15cm, some up to 30 cm (0.001cm or 0.01mm)
  • Digital micrometer screw gauge - Typically less than 2.5cm (0.0001cm or 0.001mm)
• • Planet Earth (diameter) = 10^7m
  • Moon (diameter) = 10^6m
  • Height of tall mountain = 10^3m
  • Length of football field = 10^2m
  • Height of chair = 10^-1m
  • Width of paper = 10^-4m
  • Size of human cell = 10^-6m
  • Size of large molecule = 10^-9m
• Common errors:

  Parallax error - Due to the incorrect positioning of the eyes when taking readings. Can be reduced by positioning the eyes directly above the markings.

  Zero error - due to the imperfect alignment of the zero marks between the main and smaller scales. Can be eliminated by checking for it before and after taking a measurement and accounting for it when calculating the actual length.
• Measurement of Time:

  • The digital stopwatch is the most common instrument used for measuring time.
  • Although most can provide time precise to two decimal places/0.01s, measurement error can be introduced as a result of human reaction time.
  • Human reaction time is between 0.3s to 0.5s
• Pendulum: used to measure time after it is calibrated. 1 complete oscillation of the swinging pendulum comprises it moving from one end of the swing to the other.

  
• Period: Time taken for one complete oscillation.

  • The length of the pendulum increases, so the period increases.
  • Can be determined by measuring its length. The longer the length of the pendulum, the longer its period.

  L - length of a pendulum

  G - Gravitational field strength. i.e. On Earth, g=10N/kg; On Moon, g=1.6N/kg

  • Record the time for several oscillations, then obtain the average for 1 oscillation.