Fundamentals of Physics I

Professor Shankar introduces the core concepts of Newtonian mechanics, distinguishing between kinematics and dynamics. The lecture reviews fundamental calculus applications to derive and interpret equations of motion for particles in one dimension, focusing on constant acceleration scenarios.

Professor Shankar introduces vectors in two and three dimensions, covering properties like magnitude, direction, null vectors, and unit vectors. The lecture then applies vector differentiation to analyze velocity and projectile motion.

This lecture systematically introduces Newton's three laws of motion, defining inertial frames, detailing the relationship between force and acceleration (F=ma), and explaining action-reaction pairs. Concepts of various forces and weightlessness are also examined.

This lecture extends the application of Newton's three laws to systems involving kinetic and static friction, inclined planes, and pulley dynamics. It concludes with an analysis of forces in uniform circular motion scenarios.

This lecture elaborates on the Work-Energy Theorem and the Law of Conservation of Energy, analyzing kinetic and potential energy transformations. It includes an examination of friction's impact on energy conservation and a review of relevant calculus concepts.

This lecture extends the Law of Conservation of Energy to higher dimensions, introducing work in 2D, defining conservative and non-conservative forces, and applying the cross derivative test for potential energy equations.

This lecture presents Kepler's three laws of planetary motion and systematically derives the inverse-square law of gravitational force. It further develops the equations for orbital period and velocity, and examines the conservation of energy in distant gravitational fields.

Professor Shankar elucidates the dynamics of multi-body systems, deriving the center of mass and applying the Law of Conservation of Momentum to phenomena such as the rocket equation and various types of collisions, including perfectly elastic and inelastic cases.

This lecture introduces rigid body rotation in two dimensions, defining angular velocity, momentum, acceleration, and torque. The Parallel Axis Theorem is also expounded.

This session thoroughly explains the Parallel Axis Theorem, demonstrating its application to moments of inertia for rigid bodies like a disk, alongside examining angular momentum and velocity.

This lecture explores the analogue to Newton's law, "tau = I alpha," focusing on static equilibrium scenarios where net torque is zero. The concept is demonstrated using a seesaw and multiple-object systems.

This lecture introduces the historical context and fundamental problems of relativity, analyzing events from multiple observer perspectives. It covers Maxwell's theory and the Galilean and Lorentz transformations.

This lecture provides a detailed analysis of Lorentz transformations, demonstrating how length, time, and simultaneity are relative concepts. It also addresses the Twin Paradox.

This session introduces the concept of the four-vector, unifying space-time coordinates into an entity whose components transform under Lorentz transformations. It explains the invariant space-time interval and the energy-momentum four-vector.

Continuing the discussion on four-vectors, this lecture focuses on the energy-momentum of a particle. It elaborates on the invariance of the energy-momentum four-vector due to invariant rest mass under coordinate transformations.

This lecture introduces the Taylor series and its properties through various examples. It also details complex numbers in polar form and concludes with an examination of simple harmonic motion fundamentals.

This lecture focuses on simple harmonic motion, defining amplitude, frequency, and period through examples like a mass-spring system. Several oscillation problems are solved to illustrate various cases.

Continuing with harmonic motions, this lecture solves oscillation problems and introduces the nature and behavior of waves. It defines and explains both longitudinal and transverse waves.

This lecture delves deeper into wave properties, including velocity, energy, intensity, and frequency, through diverse examples. It then focuses on wave superposition, defining constructive and destructive interference.

This lecture covers fluid dynamics and statics, discussing density and pressure, and demonstrating Archimedes' Principle. The session culminates with an introduction to Bernoulli's Equation.

This introductory thermodynamics lecture clarifies the concept of temperature, explains Zeroth's law, and defines absolute zero and the triple point of water. It also covers heat, convection, and conduction.

This lecture continues thermodynamics, detailing heat generation and measurement, introducing the Boltzmann Constant, and defining temperature microscopically. It concludes with the presentation of the First Law of Thermodynamics.