Lecture Notes: Introduction to Physics by Professor Ramamurti Shankar

Course Overview

• Course Content: Year-long introduction to major ideas in physics
  • From Galileo and Newton to revolutions in relativity and quantum mechanics
• Target Audience: Very broad, inclusive of various majors and future career paths

Importance of Physics for Diverse Careers

• Useful to know about fundamental physics, regardless of future profession
  • Examples given: doctors and special relativity/quantum mechanics

Course Structure and Organization

• Lecture Schedule: Mondays and Wednesdays from 11:30-12:45
• Course Website: Essential for accessing materials and problem sets
• Homework: Assigned on Wednesdays, due the following Wednesday
  • Head TA: Mara Daniel; collect and return graded homework
• Grading Breakdown:
  • Homework: 20%
  • Midterm: 30% (around October 20th)
  • Final: 50%
  • Amnesty Plan: Final exam score can completely determine course grade if higher
• Teaching Assistants and Discussion Sections:
  • Mark Caprio: Tuesdays 1:00-2:00 PM (Sloane Lab)
  • Steve Furlanetto: Tuesdays 8:00-10:00 PM (Dunham Lab, Room 220)

Tips for Success in the Course

• Attend lectures and refer to the book
• Prioritize doing homework - real learning happens in solving problems
  • Collaboration is encouraged
  • Utilize the undergraduate lounge and TAs
• Avoid disrupting the class
• Sleep in class is allowed but with restrictions

Calculus Requirement

• Basic knowledge of differential calculus is essential
• Understanding of functions, derivatives, and trigonometry is necessary
• Textbook appendix can serve as a guide for necessary mathematical concepts

Newtonian Mechanics

• Objective: Predict the future given the present using Newton's laws
• Key Topics:
  • Kinematics: Description of present (initial conditions)
  • Dynamics: Explanation of changes (forces causing motion)
• Kinematics: Space (x) vs. Time (t) graphs
• Important Concepts:
  • Average velocity and acceleration
  • Instantaneous velocity (derivative of position)
  • Instantaneous acceleration (second derivative of position)

Example Problem: Constant Acceleration

• Scenario: Object thrown upwards from a building
  • Building height: 15 meters
  • Initial velocity: 10 m/s
  • Acceleration due to gravity: -10 m/s² (approximated for simplicity)
• Formulas:
  • Position: x(t) = x0 + v0 t + 1/2 at²
  • Velocity: v(t) = v0 + at
  • Range formula: v² = v0² + 2a (x - x0)
• Solution Steps:
  • Determine maximum height: Time when velocity is 0
  • Calculate time to hit the ground: Set position to zero and solve
  • Analyze velocity and other dynamic properties

Methodologies and Mathematical Derivations

• Use of calculus to derive kinematic equations
• Application of derivatives and integrals to solve problems
• Approximations and simplifications
  • Example: Ignoring finer details or using g ≈ 10 m/s² instead of 9.8 m/s² for ease

Final Remarks

• Importance of understanding foundational physics principles and thinking like a physicist
• Encouragement to engage actively in learning and problem-solving