Introductory Physics Concepts

Jul 9, 2024

Introductory Physics Concepts

Topics Covered

  • Unit Conversion
  • Kinematics
  • Vectors
  • Projectile Motion
  • Newton's Laws of Motion
  • Circular Motion
  • Work and Energy
  • Linear Momentum
  • Rotational Motion

Unit Conversions

Common Conversions

  • **Mass and Length: **
    • 1 kilogram = 1000 grams
    • 1 kilometer = 1000 meters
    • 1 mile = 5280 feet
    • 1 inch = 2.54 centimeters
    • 12 inches = 1 foot
    • 3 feet = 1 yard
    • 1 meter = 100 centimeters

Conversion Examples

  • **Grams to Kilograms: **
    • 470 grams = 0.47 kilograms
  • **Centimeters to Meters: **
    • 4.6 cm = 0.046 meters
  • **Kilometers per Hour to Meters per Second: **
    • 25 km/hr = 6.94 m/s

Units of Length, Area, and Volume

  • Distance: meters (m)
  • Area: square meters (m²)
  • Volume: cubic meters (m³)

Examples:

  • Square Feet to Square Yards:
    • 36 ft² = 4 yd²
  • Cubic Inches to Cubic Feet:
    • 288 in³ = 0.167 ft³

Metric System Prefixes

  • Terra (T): 10¹²
  • Giga (G): 10⁹
  • Mega (M): 10⁶
  • Kilo (k): 10³
  • Hecto (h): 10²
  • Deca (da): 10¹
  • Base Unit (meters, liters, grams, etc.)
  • Deci (d): 10⁻¹
  • Centi (c): 10⁻²
  • Milli (m): 10⁻³
  • Micro (μ): 10⁻⁶
  • Nano (n): 10⁻⁹
  • Pico (p): 10⁻¹²

Metric System Examples

  • Millimeters to Micrometers:
    • 4.3 x 10⁻⁴ mm = 0.43 μm
  • Micrometers to Kilometers:
    • 2.6 x 10¹¹ μm = 260 km

Kinematics

Distance vs Displacement

  • Distance: Scalar, always positive
  • Displacement: Vector, has magnitude and direction

Speed vs Velocity

  • Speed: Scalar, distance/time
  • Velocity: Vector, displacement/time

Acceleration

  • Acceleration: rate of change of velocity; a = Δv/Δt

Kinematic Equations for Constant Acceleration

  1. v = u + at
  2. s = ut + ½at²
  3. v² = u² + 2as
  4. s = vt - ½at²
  5. s = ½(u + v)t

Example Problems

  • Displacement and Distance Calculation:

    • Eastward: +10 miles
    • Westward: -18 miles
    • Eastward: +3 miles
    • Total Displacement: -5 miles
    • Total Distance: 31 miles

  • Acceleration Calculation

    • Initial Speed = 10 m/s
    • Final Speed = 40 m/s
    • Time = 5 seconds
    • Acceleration: 6 m/s²

Newton's Laws of Motion

Newton's 1st Law

  • Law of Inertia:
    • An object at rest stays at rest, and an object in motion remains in motion unless acted on by a net external force.

Newton's 2nd Law

  • F = ma:
    • Force = mass × acceleration

Newton's 3rd Law

  • Action/Reaction:
    • For every action, there is an equal and opposite reaction.

Friction

  • Static Friction: When objects are not moving relative to each other.
  • Kinetic Friction: When objects are moving relative to each other.
  • **Formulas: **
    • fₛ ≤ μₛN
    • fₖ = μₖN

Energy

Types of Energy

  • Kinetic Energy (KE): ½mv²
  • Potential Energy (PE): mgh
  • Mechanical Energy (ME): KE + PE

Conservation of Mechanical Energy

  • Gravity: Conservative force. Mechanical energy remains constant when only gravity does work.
  • Friction: Non-conservative force. Reduces mechanical energy.

Work

  • Definition:
    • Work = force × distance
  • Work-Energy Theorem:
    • Work done = Change in kinetic energy

Momentum

Linear Momentum

  • Definition: p = mv
  • Impulse-Momentum Theorem:
    • Impulse = Δp = FΔt

Conservation of Momentum

  • Elastic Collisions: Kinetic energy is conserved.
  • Inelastic Collisions: Kinetic energy is not conserved, but momentum is.
  • Formula:
    • m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Circular Motion

Centripetal Force

  • Definition:
    • F = mv²/r
  • Centripetal Acceleration:
    • a = v²/r

Gravitational Force and Orbital Motion

  • Formula:
    • F_gravity = G(m₁m₂/r²)
    • G = 6.67430 × 10⁻¹¹ m³⋅kg⁻¹⋅s⁻²
  • Speed of Orbiting Object:
    • v = √(GM/r)

Miscellaneous

  • **Maximum Safe Speed for a Car in a Curve: **
    • μₛg = v²/r
  • Force in Horizontal Circular Motion:
    • T = mv²/r (Tension provides the force)

Rotational Motion

Key Equations

  • Torque: τ = F × l
  • Rotational Work: W = τθ
  • Angular Displacement: θ = ωt
  • Angular Velocity: ω = ω₀ + αt
  • Angular Acceleration: α = Δω/Δt

Inertia

  • Formula for a disk: I = ½mR²
  • Formula for a sphere: I = ²/₅ mR²

For additional practice problems and detailed videos, refer to the channel's physics playlists.