Physics 20 Review Notes

Kinematics

• Graphing Interpretations:
  • Slope of displacement-time graph = velocity.
  • Slope of velocity-time graph = acceleration.
  • Area under velocity-time graph = displacement.
• Scalar vs. Vector:
  • Scalar: Magnitude only.
  • Vector: Magnitude and direction.
• Uniform Motion:
  • Constant velocity.
  • v = \frac{\Delta d}{\Delta t}
• Uniformly Accelerated Motion:
  • Acceleration: Rate of change in velocity.
  • Speeding up: Acceleration and velocity vectors in same direction.
  • Slowing down: Acceleration and velocity vectors in opposite directions.
  • Instantaneous velocity: Velocity at a specific time.
  • Free-fall: Acceleration due to Earth’s gravity (9.81 m/s²).
• Projectiles:
  • Object moving under gravity.
  • Horizontal (x-axis) and vertical (y-axis) components are independent, except for time.
  • Horizontal component: uniform motion.
  • Vertical component: uniform acceleration.
  • Common Scenarios
    • Object dropped straight down
    • Object thrown directly upward
    • Object launched horizontally
    • Object launched at an angle

Dynamics

• Dynamics: Study of forces.
• Force: Push or pull that changes an object’s velocity.
• Newton’s Laws of Motion:
  • 1st Law (Inertia): Object maintains constant velocity unless acted upon by unbalanced force.
  • Inertia: Resistance to acceleration.
  • 2nd Law: Unbalanced force causes acceleration.
  • 3rd Law (Action-Reaction): Forces occur in pairs, equal and opposite.
• Mass vs. Weight:
  • Mass: Amount of matter.
  • Weight: Force due to gravity (F_g).
• Net Force (\sum F):
  • Vector sum of forces.
  • \sum F = F1 + F2 + F_3 + …
• Free-Body Diagrams (FBD):
  • Visualize forces acting on an object.
  • Includes:
    • Types of forces
    • Direction of forces
    • Relative magnitude of forces
  • Common Forces:
    • F_g: Weight
    • F_n: Normal force (perpendicular to surface), apparent weight.
    • T: Tension (rope, string, cable).
    • F_s: Elastic force (compression or extension).
    • F_f: Friction (opposes motion).
• Friction:
  • Static (stationary) and kinetic (sliding).
  • Solved in F_{net} statements.
  • Formula: Ff = \mu Fn

Circular Motion & Gravitation

• Centripetal Force (F_c):
  • Center-seeking force, radially inward.
  • Net force caused by agents like friction, tension, or gravity.
• Time Period (T) & Frequency (f):
  • f = \frac{1}{T}
  • Period (T): Time for one revolution (seconds).
  • Frequency (f): Revolutions per second (Hertz).
• Kepler’s Laws of Planetary Motion:
  • Law of Ellipses: Planets orbit the sun in ellipses with the Sun at one focus.
  • Law of Equal Areas: A line connecting the Sun and a planet sweeps equal areas during equal time intervals.
  • \frac{R^3}{T^2} = K
• Universal Gravitation - Force of Gravity (F_g):
  • Attractive force between objects with mass.
  • Proportional to mass.
  • Inversely proportional to the square of the distance (inverse square law).
  • Fg \propto \frac{m1 m_2}{r^2}
• Universal Gravitation - Gravitational Field:
  • Field: Region of influence.
  • Explains gravitational force at a distance.
  • Equations for gravitational field:
    • g = \frac{F_g}{m}
    • g=\frac{GM}{r^2}

Energy

• Work & Energy:
  • Energy: Ability to do work.
  • W = F \cdot d = \Delta E
  • Work: Change in energy or product of force and displacement.
  • Force and displacement must be in the same axis.
• Systems:
  • Open: Matter and energy can enter and leave.
  • Closed: Only energy can enter and leave.
  • Isolated closed: Neither matter nor energy can enter or leave.
• Power (P):
  • Rate of energy conversion or doing work.
  • P = \frac{\Delta E}{t} = \frac{W}{t}
• Mechanical Energy:
  • Kinetic and potential energy.
  • Potential energy: Gravitational and elastic.
• Law of Conservation of Energy:
  • Energy cannot be created or destroyed, only transformed.
  • In an isolated closed system, energy is conserved.
  • \sum E{\text{initial}} = \sum E{\text{final}}
  • \sum Ek + \sum Ep = \text{constant}
  • \Delta E = \Delta Ek + \Delta Ep + W_s = 0

SHM & Waves

• SHM & Periodic Motion:
  • Simple Harmonic Motion (SHM): Restoring force proportional to displacement from equilibrium.
  • f = \frac{1}{T}
  • Period: Time for one cycle.
  • Frequency: Cycles per time.
• Springs & Pendulums:
  • Ideal examples of periodic motion & SHM.
• Wave Basics:
  • Source: Vibrates to create disturbance (determines frequency).
  • Medium: Substance wave travels through.
  • Wavelength (λ): Distance between equivalent positions.
  • Amplitude: Wave’s maximum displacement from equilibrium.
  • Universal Wave Equation:
    • v = \lambda f
    • \lambda = vT
• Wave Types:
  • Two types of mechanical waves: Transverse & Longitudinal.
• Wave Properties:
  • Reflection: Part of wave that doesn’t cross boundary. Reflected angle = incident angle.
  • Refraction: Part of wave that crosses boundary. Snell’s law:
    • \frac{\sin \thetai}{\sin \thetar} = \frac{vi}{vr} = \frac{\lambdai}{\lambdar} = \frac{nr}{ni}
  • Diffraction: Wave spreading through opening or around corner.
  • Interference: Waves meet and superimpose constructively (larger) or destructively (smaller).
• Resonance & Air Columns:
  • Resonance: Vibration when object experiences periodic force, creating a standing wave.
  • Standing wave: Nodes (destructive) and antinodes (constructive) at steady positions.
• Doppler Effect:
  • Apparent frequency shift when wave source is in motion.