Unit 2: Physical Quantities

Physical quantities are properties of phenomena or matter that can be measured and described quantitatively using numbers and units. This unit covers the fundamental principles of measurement, including the use of various scales, the definition of international standards, and the classification of quantities as basic or derived. Mastery of these concepts is essential for performing accurate scientific experiments and communicating data effectively through scientific notation and significant figures.

2.1 Scales, Standards, Units (prefixes)

• Scale: A set of markings on a measurement device that represents the amount of the property being measured.
• The precision of a measurement device increases as the number of marks on the scale increases.
• Standard: A clearly defined and readily accessible property used for reliable comparison in measurement across different locations and times.
• SI system of units: An adaptation of the metric system established in 2019 to provide international standards for basic quantities.
• Meter (m): The standard unit of length, defined as the distance traveled by light in a vacuum during a specific time interval ($1/299,792,458$ seconds).
• Kilogram (kg): The standard unit of mass, defined using the fixed numerical value of the Planck constant ($h$).
• Second (s): The standard unit of time, defined based on the period of vibration of radiation from the caesium-133 atom.
• Scientific notation: A method of writing very large or small numbers in the form $d \times 10^n$, where $d$ is a number between 1 and 10.
• Significant figures: Each non-zero digit in a measured value, including zeros between non-zero digits or at the end of a decimal part, representing the precision of the measurement.
• Prefix: A letter or syllable written directly before a unit to indicate multiples or fractions of the base unit (e.g., kilo-, milli-).

2.2 Measurement and Safety

• Measurement: The process of comparing an unknown quantity with a known fixed unit quantity of its kind.
• A measurement consists of two parts: a numerical value (magnitude) and a unit.
• Length: A basic physical quantity describing the distance between two points.
• Mass: The amount of matter contained in a body, measured using instruments like a beam balance.
• Time: A basic physical quantity describing the duration between the beginning and end of an event.
• Laboratory safety rules: Guidelines to ensure safe experimentation, such as wearing lab safety goggles, never working alone, and reporting accidents immediately.

2.3 Classification of Physical Quantities

• Fundamental (basic) physical quantities: Quantities that can be measured directly and cannot be described in terms of other quantities.
• There are seven fundamental quantities: length, mass, time, temperature, current, amount of substance, and luminous intensity.
• Derived physical quantities: Quantities that depend on one or more fundamental quantities for their measurement (e.g., area, volume, density, and speed).
• Scalar quantity: A physical quantity that is described completely by magnitude (number and unit) alone.
• Vector quantity: A physical quantity that requires both magnitude and direction for its complete description.

2.4 Unit Conversion

• Conversion of units: The process of changing between different units for the same physical quantity using multiplicative conversion factors.
• Units can be converted from the SI system to non-SI systems and vice versa to suit specific measurement needs.

Process: Determining Measured Values from an Analog Scale

1. Identify the numbered values on the scale and determine the difference between them.
2. Count the number of spaces between the numbered values to find the value represented by each smaller mark.
3. Read the scale to the nearest marked value.
4. Estimate the last digit between the smallest markings to increase measurement precision.

Process: Applying Significant Figure Rules in Calculations

1. For multiplication or division, identify the number of significant figures in each starting quantity.
2. Perform the calculation.
3. Round the final answer so it has the same number of significant figures as the quantity with the smallest number of significant figures.

Key Terminology

• Physical quantity: Anything that can be measured and described by a number and unit.
• Scale: A set of numbers or markings used to measure or compare levels.
• Standard: A reliable, measurable property chosen as an international reference.
• SI system of units: The international standard system for measurement.
• Meter: The SI unit of length.
• Kilogram: The SI unit of mass.
• Second: The SI unit of time.
• Scientific notation: Writing numbers as products of a decimal (1-10) and a power of 10.
• Significant figures: Digits in a number that carry meaningful information about its precision.
• Prefix: A syllable written before a unit to modify its magnitude.
• Measurement: Comparison of an unknown quantity with a known unit.
• Length: Distance between two points.
• Mass: The amount of matter in a body.
• Time: Duration between the beginning and end of an event.
• Fundamental (basic) physical quantities: Directly measurable quantities not derived from others.
• Fundamental units: Units used to measure basic quantities.
• Derived physical quantities: Quantities calculated from basic quantities.
• Derived units: Units of measurements for derived quantities.
• Scalar quantity: A quantity with magnitude only.
• Vector quantity: A quantity with both magnitude and direction.
• Magnitude: The number and unit describing a quantity’s size.