1 Physical Units (AS)

1.1 Physical quantities

• Physical quantities consist of a numerical magnitude and a unit, they represent measurable aspects of the physical world.
• They include quantities like length, mass, time, temperature, velocity, and force.
• Each physical quantity has a specific unit of measurement associated with it.

1.2 SI units:

1.2.1 SI base quantities and units:

• The International System of Units (SI) is the globally recognized standard for measuring physical quantities.
• SI base quantities are the fundamental physical quantities from which all other quantities are derived.
• The SI base quantities and their units are as follows:
  • Mass (kg) measures the amount of matter in an object.
  • Length (m) measures the distance between two points.
  • Time (s) measures the duration or interval between events.
  • Electric Current (A) measures the flow of electric charge.
  • Temperature (K) measures the average kinetic energy of particles in a substance.

1.2.2 Derived units:

• Derived units are obtained by combining SI base units using multiplication or division.
• Examples of derived units include:
  • Area (m²) is derived from length squared.
  • Volume (m³) is derived from length cubed.
  • Speed (m/s) is derived from distance divided by time.
  • Acceleration (m/s²) is derived from change in velocity divided by time.
• It is important to use the appropriate derived units when dealing with derived quantities.

1.2.3 Prefixes:

• Prefixes are used to indicate decimal submultiples or multiples of both base and derived units.
• Commonly used SI prefixes and their symbols include:
  • Pico (p) for 10^(-12)
  • Nano (n) for 10^(-9)
  • Micro (μ) for 10^(-6)
  • Milli (m) for 10^(-3)
  • Centi "c" for 10^(-2)
  • Deci (d) for 10^(-1)
  • Kilo (k) for 10^(3)
  • Mega (M) for 10^(6)
  • Giga (G) for 10^(9)
  • Tera (T) for 10^(12)
• These prefixes help express quantities that are either very small or very large more conveniently.

1.3 Errors and uncertainties:

1.3.1 Types of errors:

• Systematic errors are consistent and occur due to flaws in measurement equipment or experimental setup. They affect all measurements in the same way.
• Random errors are unpredictable and can arise from factors like human limitations, environmental conditions, or inherent variability in the measured quantity. They cause fluctuations in repeated measurements.

1.3.2 Precision and accuracy:

• Precision refers to the degree of consistency or reproducibility of measurements. Precise measurements have little variation between repeated values.
• Accuracy reflects how close a measurement is to the true value. Accurate measurements have small systematic errors.

1.3.3 Uncertainty in derived quantities:

• When combining measurements to calculate derived quantities, uncertainties also propagate.
• Uncertainty in a derived quantity can be estimated by adding absolute or percentage uncertainties from the measured quantities involved.

1.4 Scalars and vectors:

1.4.1 Scalars:

• Scalars are quantities that have only magnitude and no direction.
• Examples of scalar quantities include mass, time, temperature, and energy.

1.4.2 Vectors:

• Vectors are quantities that have both magnitude and direction.
• Examples of vector quantities include displacement, velocity, acceleration, and force.

1.4.3 Vector addition and subtraction:

• Coplanar vectors (vectors lying in the same plane) can be added or subtracted by using graphical or algebraic methods.

1.4.4 Vector components:

• A vector can be represented as the sum of two perpendicular components.
• The horizontal and vertical components of a vector help analyze its effects along different axes or directions.