Formulae Measurements

FORMULAE MEASUREMENTS: LENGTH AND INSTRUMENT READINGS

  • Vemier Caliper Measurement Formula:

    • General formula for calculating length using a Vemier Caliper:         Total Reading=Ms+Vs\text{Total Reading} = \text{Ms} + \text{Vs}
    • Parameter definitions:
      • Ms\text{Ms}: Main scale reading.
      • Vs\text{Vs}: Vernier scale reading.
    • Worked Example:
      • Main scale reading (Ms\text{Ms}): 12 mm12\,\text{mm}
      • Vernier scale reading (Vs\text{Vs}): 0.7 mm0.7\,\text{mm}
      • Calculation:             12 mm+0.7 mm=12.7 mm12\,\text{mm} + 0.7\,\text{mm} = 12.7\,\text{mm}

  • Macrometer Screw Gauge Measurement Formula:

    • General formula for calculating thickness or diameter using a Macrometer screw gauge:         Total Reading=Ms+(Thimble scale reading×0.01)\text{Total Reading} = \text{Ms} + (\text{Thimble scale reading} \times 0.01)
    • Parameter definitions:
      • Ms\text{Ms}: Main scale reading.
      • Thimble scale reading\text{Thimble scale reading}: Reading taken directly from the circular thimble scale.
      • 0.010.01: Scale factor / precision multiplier for the thimble reading.
    • Worked Example:
      • Main scale reading (Ms\text{Ms}): 7.57.5
      • Thimble scale reading: 55
      • Calculation setup:             7.5+(5×0.01)7.5 + (5 \times 0.01)
      • Evaluated calculation:             7.5+0.05=7.557.5 + 0.05 = 7.55

PERIOD, OSCILLATION, AND FREQUENCY FORMULAE

  • Period (Peaed, TT):

    • General formula for calculating the period from oscillation timing:         T=time takennumber of oscillationsT = \frac{\text{time taken}}{\text{number of oscillations}}(also noted as time baken)
    • Relationship between Period (TT) and Frequency (FF):         T=1FT = \frac{1}{F}
    • Worked Example:
      • time taken=20\text{time taken} = 20
      • number of oscillations=10\text{number of oscillations} = 10
      • Calculation:             T=2010=2 seconds per oscillationT = \frac{20}{10} = 2\,\text{seconds per oscillation}

  • Frequency (FF):

    • General formula defining frequency as the reciprocal of the period:         F=1TF = \frac{1}{T}
    • Worked Example:
      • Given period value: T=2T = 2
      • Calculation:             F=12=0.5 HerbzF = \frac{1}{2} = 0.5\,\text{Herbz}

TIME MEASUREMENT AND UNIT CONVERSIONS

  • Total Time Calculation Formula:

    • General conversion relation to combine minutes, seconds, and sub-second units into total seconds:         Total Time=(Min×60 s)+Seconds+Mini Seconds10/100/1000\text{Total Time} = (\text{Min} \times 60\,\text{s}) + \text{Seconds} + \frac{\text{Mini Seconds}}{10 / 100 / 1000}
    • Component breakdown:
      • Min×60 s\text{Min} \times 60\,\text{s}: Converts the minute portion to seconds.
      • Seconds\text{Seconds}: Base seconds measurement added directly.
      • Mini Seconds10/100/1000\frac{\text{Mini Seconds}}{10 / 100 / 1000}: Conversion of fractional seconds or Mini Seconds using decimal divisors (1010, 100100, or 10001000 depending on scale resolution).

  • Step-by-Step Worked Conversion Example:

    • Input components:
      • Minutes: 3 Min3\,\text{Min}
      • Seconds: 175 s175\,\text{s}
      • Mini Seconds: 8181 over a base denominator of 100100
    • Full substitution formula:         (3×60)+175+81100(3 \times 60) + 175 + \frac{81}{100}
    • Step 1: Evaluate the minute term:         3×60=1803 \times 60 = 180
    • Step 2: State the direct seconds term:         175175
    • Step 3: Evaluate the Mini Seconds fractional term:         81100=0.81\frac{81}{100} = 0.81
    • Step 4: Sum all evaluated terms to obtain the total time:         180+175+0.81=355.81 s180 + 175 + 0.81 = 355.81\,\text{s}(recorded as 355.815355.815)