Introduction to Physics - Professor Ramamurti Shankar Lecture Notes

Course Overview

• Course Duration: Year-long
• Content: Major ideas in physics from Galileo and Newton to relativity and quantum mechanics.
• Target Audience: Broad, including non-physics majors.
• Purpose: To learn about the biggest and most interesting revolutions in physics.

Course Logistics

• Class Schedule: Monday and Wednesday, 11:30-12:45.
• Lecture Recording: Lectures are taped as part of an experimental pilot program funded by the Hewlett Foundation.
• Course Communication: Information and communications posted on the course website.
• Homework: Assigned on Wednesday, due before the next class. Solutions posted the same afternoon.
• Head TA: Mara Daniel (formerly Mara Baraban).
• Grading:
  • Homework: 20%
  • Midterm: 30% (October)
  • Final Exam: 50%
  • Amnesty Plan: Overall grade can be the higher of the weighted average or the final exam grade alone.

Additional Support

• Discussion Sections:
  • Mark Caprio: Tuesdays 1:00-2:00 pm in Sloane Lab.
  • Steve Furlanetto: Tuesday night in Dunham Lab, Room 220.
• Office Hours: To be determined based on student availability.
• Undergraduate Lounge: TA support available daily.

Advice for Success

• Attend Lectures: Useful for understanding essential parts of the material not covered in the textbook.
• Do Homework: Homework helps gauge understanding and is crucial for doing well in physics.
• Work in Groups: Collaboration is encouraged, but ensure individual understanding.
• Participate in Labs: Labs are important for understanding experimental aspects of physics.
• Classroom Etiquette: Minimize talking; it distracts. Sleeping is okay if non-disruptive.
• Ask Questions: Stopping the lecturer for questions is encouraged.

Mathematics Requirement

• Prerequisite Knowledge:
  • Differential calculus: Functions, derivatives, second derivatives, basic integrals.
  • Trigonometry: Sine, cosine, and related identities.

Newtonian Mechanics

• Focus: Starting with simple examples, then gradually adding complexity.
• Goals: Predict the future given the present by understanding initial conditions.
• Key Concepts:
  • Kinematics: Description of the present state (position, velocity).
  • Dynamics: Understanding the forces causing the motion.

Kinematics

• Position and Velocity:
  • Position (x) as a function of time (t).
  • Velocity (v) as the derivative of position: v = dx/dt.
  • Acceleration (a) as the derivative of velocity: a = d²x/dt².
• Graph Interpretation: x vs. t graph shows motion over time.
• Constant Acceleration: Important in problems like free fall under gravity (a = -g).

Key Equations

• Position with Constant Acceleration:
  • x(t) = x₀ + v₀t + ½at²
• Velocity with Constant Acceleration:
  • v(t) = v₀ + at
• Eliminating Time:
  • v² = v₀² + 2a(x - x₀)

Problem-Solving Example

• Scenario: Object thrown upwards from a height of 15 meters with an initial velocity of 10 m/s.
• Objective: Predict its motion using the equations of kinematics.
• Calculation:
  • Find Maximum Height: Use v = 0 at the highest point.
  • Time to Hit Ground: Solve for t when y = 0.
  • Speed Upon Impact: Use the derived kinematic equations.

Tips for Using Equations

• Understand Limitations: Equations are valid under specific assumptions (e.g., constant acceleration).
• Use in Context: Apply appropriately, considering physical scenarios and conditions.

Final Remarks

• Engagement: Actively follow the logic and anticipate steps in problem-solving.
• Mathematical Rigor: Understand and apply calculus concepts appropriately for physics problems.
• Class Resources: Utilize the website for problems and additional course materials.