topic 1 physics

Measurement Principles

  • Scientific Method: Guides scientists' observations and measurements.

  • S.I. System: System of International Units defining 7 fundamental quantities:

    • Length (metre, m)

    • Mass (kilogram, kg)

    • Time (second, s)

    • Electric Current (ampere, A)

    • Temperature (kelvin, K)

    • Luminous Intensity (candela, cd)

    • Amount of Matter (mole, mol)

Units of Measurement

  • Derived Units: Combination of fundamental units (e.g., velocity = distance/time = m/s).

  • Measurement Uncertainty: All measurements have some degree of error;

    • Absolute Error: Half of instrument's limit of reading.

    • Example: Ruler with limit of 1 mm has ±0.5 mm error.

Error Calculations

  • Relative Error: Compares absolute error to measured value.

    • Formula: Relative Error = Absolute Error / Measured Value

    • Example: If measuring 8 mm with an error of ±0.5 mm, relative error = 0.5/8 = 0.0625, percentage error = 6.25%.

Rounding Numbers

  • Reduces number of digits while aiming to preserve value.

  • Example: Round 4837 to nearest ten:

    • Identify last digit to keep (3); next digit is 7 → increase to 4 → 4840.

  • Rounding rules applied to significant figures (SF).

Significant Figures

  • SF: Digits known with certainty plus the first uncertain digit.

  • Example: A reading of 265.3 mm has 4 significant figures.

  • When performing calculations, results must reflect the least number of SF in the data used:

    • Example: 28.5 + 1.432 = 29.932 → 29.9 (3 SF).

Zero Rules in Significant Figures

  • Significant:

    • All non-zero digits.

    • Zeros between digits (e.g., 2005).

  • Non-Significant:

    • Leading zeros (e.g., 0.03 has 1 SF).

    • Trailing zeros in whole numbers without a decimal (e.g., 7800 has 2 SF).

    • Use scientific notation for clarity (e.g., 360 = 3.60 × 10^2 has 3 SF).

Reading and Measurement Instruments

  • Instruments: Accuracy increases from rulers (1 mm) → vernier scale (0.1 mm) → micrometer (0.01 mm).

  • More precise measuring results with each advance in instrument type.