Study Notes: Physics 101

Physical Quantities

  • Measurable quantities, e.g., length, mass, time.
  • Types:
    • Fundamental: Not derived from others (e.g., mass, length, time).
    • Derived: Formed from fundamental quantities (e.g., velocity).

Units

  • Standard measures for physical quantities:
    • Fundamental units: Mass, length, time.
    • Derived units: Expressed in fundamental units (e.g., speed: m/s).

Systems of Units

  1. CGS: Centimetre, gram, second.
  2. FPS: Foot, pound, second.
  3. MKS: Metre, kilogram, second.

Dimensional Analysis

  • Dimensions express physical quantities in terms of fundamental quantities.
    • Example: Force = $[M][L][T^{-2}]$.
  • Dimensional formula shows base quantities involved:
    • Area: $[M^0 L^2 T^0]$.
    • Volume: $[M^0 L^3 T^0]$.
  • Homogeneity Principle: Equations must have consistent dimensions.

Motion

  • Definitions:
    • Motion: Change in position over time.
  • Types:
    1. One-dimensional (rectilinear).
    2. Two-dimensional (plane).
    3. Three-dimensional (space).

Kinematic Equations

  • For uniformly accelerated motion:
    1. $v = v_0 + at$
    2. $x - x0 = v0 t + \frac{1}{2} a t^2$
    3. $v^2 = v0^2 + 2a(x - x0)$

Vectors

  • Scalars: Quantities with magnitude only (e.g., mass).
  • Vectors: Quantities with magnitude and direction (e.g., force).

Projectile Motion

  • Trajectory: Parabolic path:
    • Horizontal range: $R = \frac{v_0^2 \sin 2\theta}{g}$.
    • Max height: $H = \frac{v_0^2 \sin^2 \theta}{2g}$.

Laws of Motion

  • Newton's First Law: Inertia; objects remain at rest or in motion unless acted upon.
  • Newton's Second Law: $F = ma$; force is the rate of change of momentum.
  • Newton's Third Law: For every action, there's an equal and opposite reaction.

Work, Energy, and Power

  • Work done: $W = F \cdot d \cos \theta$.
  • Kinetic Energy: $KE = \frac{1}{2} mv^2$.
  • Potential Energy: $PE = mgh$.
  • Power: Rate of doing work; $P = \frac{W}{t}$.

Thermodynamics

  • First Law: $\Delta Q = \Delta U + \Delta W$.
  • Stages: Isothermal, adiabatic, cyclic.
  • Ideal gas equation: $PV = nRT$.

Oscillations and Waves

  • Simple Harmonic Motion (SHM): Restoring force proportional to displacement.
    • $x(t) = A \sin(\omega t + \phi)$.
  • Wave types: Transverse and longitudinal.
  • Standing waves: Nodes and antinodes formed by interference.