Lecture on Introduction to Physics

Jul 12, 2024

Lecture on Introduction to Physics

Overview

  • Course: Year-long course in physics
  • Scope: From Galileo and Newton to relativity and quantum mechanics
  • Audience: Very broad, helpful regardless of major (doctors, various other professions)
  • Objective: Learn about revolutionary concepts in physics

Course Logistics

Recording

  • Lectures will be taped as part of a pilot program by the Hewlett Foundation
  • Lectures might be posted online later
  • Ignore the camera during lectures

Schedule and Assignments

  • Classes: Monday and Wednesday, 11:30-12:45
  • Homework: Assigned on Wednesday, due by next Wednesday before class
  • Website: Class information and homework solutions posted here
  • TA: Mara Daniel (head TA), collects and returns problem sets

Grading

  • Weightage: 20% homework, 30% midterm (in October), 50% final
  • Amnesty Plan: Final grade may override midterm and homework average

Tips for Success

  • Attend Lectures: To hear the subject presented orally
  • Read the Book: Focus on essential parts as covered in lectures
  • Do Homework: Collaborative work is encouraged, homework helps in understanding
  • Office Hours: Schedule TBD, procedural issues to be directed to TAs

Rules and Conduct

  • No Talking: Distracts the lecture, please refrain
  • Sleeping: Allowed if not disruptive (no talking in sleep, avoid domino effect)

Interactive Lectures

  • Questioning: Encouraged to ask questions at any time
  • Class Interaction: Important for better understanding and real-time feedback

Course Content

Newtonian Mechanics

  • Developed by: Sir Isaac Newton
  • Scope: Basic motion of objects (billiard balls, trucks, etc.)

Key Concepts and Mathematical Foundations

  • Kinematics: Description of motion (position, velocity, acceleration)
    • Average velocity: [ \bar{v} = \frac{\Delta x}{\Delta t} ]
    • Instantaneous velocity: [ v(t) = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt} ]
    • Instantaneous acceleration: [ a(t) = \frac{dv}{dt} = \frac{d^2x}{dt^2} ]

Equations of Motion with Constant Acceleration

  • Position: [ x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 ]
  • Velocity: [ v(t) = v_0 + at ]
  • Eliminating time: [ v^2 = v_0^2 + 2a (x - x_0) ]

Example Problem: Object thrown from a height with initial velocity

  • Given:
    • Height: 15 meters
    • Initial velocity: 10 m/s
    • Gravity: -10 m/s²
  • Findings:
    • Position at any time t: [ y(t) = 15 + 10t - 5t^2 ]
    • Velocity at any time t: [ v(t) = 10 - 10t ]
    • Max Height: 20 meters (at t = 1 sec)
    • Time to hit the ground: 3 seconds

Differential and Integral Calculus in Physics

  • Application: Use of derivatives to find instantaneous rates (e.g., velocity, acceleration)
  • Important Techniques:
    • Multiplying both sides of equations by small intervals (Δt) to find relationships
  • Concepts:
    • Difference between differentiation (algorithmic) and integration (guessing)
  • Formulas derived using integral calculus to find relationships between motion parameters