Physical science

Part 1: Chemistry — Quantitative Aspects of Chemical Change

This section covers the basics of measuring chemical quantities using moles and key formulas.

1. Key Definitions

• The Mole ($n$): The standard unit for measuring the amount of a substance. One mole contains the exact same number of particles as there are atoms in $12\,\text{g}$ of Carbon-12.

• Molar Mass ($M$): The mass of one mole of a substance, measured in $\text{g}\,\text{mol}^{-1}$.

• Avogadro's Number ($N_A$): The number of particles in one mole of a substance, equal to $6.02 \times 10^{23}\,\text{particles}\,\text{mol}^{-1}$.

• Molar Gas Volume ($V_m$): The volume occupied by one mole of any gas at standard temperature and pressure (STP), which is always $22.4\,\text{dm}^3\,\text{mol}^{-1}$.

• Empirical Formula: The simplest whole-number ratio of atoms in a compound.

2. Core Formulas

• Moles from Mass: $n = \frac{m}{M}$

  • $m = \text{mass in grams}$

  • $M = \text{molar mass}$

• Moles from Gas Volume (at STP): $n = \frac{V}{V_m}$

  • $V = \text{volume in } \text{dm}^3$

  • $V_m = 22.4\,\text{dm}^3\,\text{mol}^{-1}$

• Moles from Concentration: $n = c \times V$

  • $c = \text{concentration in } \text{mol}\,\text{dm}^{-3}$

  • $V = \text{volume in } \text{dm}^3$

Part 2: Physics — Vectors and Scalars

This section explains how to work with physical quantities that have size, units, and directions.

1. Key Definitions

• Scalar: A quantity that has magnitude (size) and a unit only (e.g., mass, time, distance, speed, energy).

• Vector: A quantity that has magnitude, a unit, and a specific direction (e.g., displacement, velocity, acceleration, force).

• Resultant Vector: A single vector that has the exact same total effect as two or more vectors combined.

2. Vector Addition Method

• For vectors acting along a straight line, pick one direction as positive ($+$).

• Example: If Right is chosen as positive ($+$), then any vector pointing Left becomes negative ($-$).

Part 3: Physics — Motion in One Dimension

This section describes how objects move in a straight line.

1. Core Differences

• Distance vs. Displacement:

  • Distance ($d$): Total length of the path traveled (Scalar).

  • Displacement ($\Delta x$): Shortest straight-line distance from start to finish, including direction (Vector).

• Speed vs. Velocity:

  • Speed ($v$): How fast distance is covered (Scalar): $v = \frac{d}{\Delta t}$

  • Velocity ($v$): Rate of change of position in a direction (Vector): $v = \frac{\Delta x}{\Delta t}$

• Acceleration ($a$): The rate at which velocity changes over time (Vector), measured in $\text{m}\,\text{s}^{-2}$:
  $a = \frac{\Delta v}{\Delta t} = \frac{v<em>f - v</em>i}{\Delta t}$

2. Equations of Motion

(Only applicable when acceleration $a$ is constant)

• $v<em>f = v</em>i + a\Delta t$

• $v<em>f^2 = v</em>i^2 + 2a\Delta x$

• $\Delta x = v_i\Delta t + \frac{1}{2}a\Delta t^2$

• $\Delta x = \left(\frac{v<em>i + v</em>f}{2}\right)\Delta t$

3. Graphs of Motion (Key Insights)

• Position vs. Time Graph: Slope (gradient) equals velocity.

• Velocity vs. Time Graph:

  • Slope (gradient) equals acceleration.

  • Area under the graph equals displacement.