1.1 Physical Quantities
A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit.
Base Quantities and SI Units
Base quantities are physical quantities that cannot be defined in terms of other physical quantities.
- Length ($l$): metre ($\text{m}$)
- Mass ($m$): kilogram ($\text{kg}$)
- Time ($t$): second ($\text{s}$)
- Thermodynamic Temperature ($T$): kelvin ($\text{K}$)
- Electric Current ($I$): ampere ($\text{A}$)
- Luminous Intensity ($I_v$): candela ($\text{cd}$)
- Amount of Substance ($n$): mole ($\text{mol}$)
Derived Quantities
Derived quantities are physical quantities derived from base quantities through multiplication, division, or both.
- Velocity ($v$): $v = \frac{s}{t} \rightarrow \text{Unit: } \text{m s}^{-1}$
- Acceleration ($a$): $a = \frac{v - u}{t} \rightarrow \text{Unit: } \text{m s}^{-2}$
- Force ($F$): $F = ma \rightarrow \text{Unit: } \text{kg m s}^{-2} \text{ or Newton (N)}$
- Density ($\rho$): $\rho = \frac{m}{V} \rightarrow \text{Unit: } \text{kg m}^{-3}$
- Pressure ($P$): $P = \frac{F}{A} \rightarrow \text{Unit: } \text{N m}^{-2} \text{ or Pascal (Pa)}$
Scalar vs Vector Quantities
- Scalar Quantity: A physical quantity that has magnitude only (e.g., Mass, Distance, Speed, Energy, Temperature, Density).
- Vector Quantity: A physical quantity that has both magnitude and direction (e.g., Displacement, Velocity, Acceleration, Force, Momentum).
1.2 Scientific Investigation & Graphical Analysis
Variables in Scientific Experiments
- Manipulated Variable (MV): The factor altered systematically.
- Responding Variable (RV): The factor measured/observed.
- Constant Variable (CV): Factors kept fixed to ensure a fair test.
Shapes of Graphs and Relationships Between Variables
- Straight line passing through the origin: $y$ is directly proportional to $x$ ($y \propto x$). Equation: $y = mx$.
- Straight line with a positive $y$-intercept: $y$ increases linearly with $x$. Equation: $y = mx + c$.
- Straight line with a negative gradient: $y$ decreases linearly with $x$. Equation: $y = -mx + c$.
- Curve decreasing smoothly without touching axes: $y$ is inversely proportional to $x$ ($y \propto \frac{1}{x}$). Equation: $y = \frac{k}{x}$.
Gradient and Area Under Graph
- Gradient ($m$): $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$. It represents the physical quantity given by the ratio of the vertical variable unit to the horizontal variable unit.
- Area under the graph: Represents the physical product of the variables on the vertical axis and horizontal axis.