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The session focused on solving physics problems related to small displacements, stable equilibrium, rotation matrices, and Lagrangian mechanics. The student practiced defining generalized coordinates, calculating kinetic and potential energies, and identifying symmetries in a sliding pendulum system. The tutor assigned follow-up work to solve the pendulum problem and aim to express the solution as an integral.

The Student and Tutor worked through a problem involving a bead on a rotating wire, focusing on kinetic and potential energy calculations, Lagrangian mechanics, and determining equilibrium points. They derived the equation of motion and discussed the stability of equilibrium points. The Student will continue working on the problem in the next session, starting with substituting a variable into the equation of motion and performing an expansion.

The session focused on Lagrangian mechanics, covering coordinate system selection for a simple pendulum and a bead on a hemispherical bowl, cyclic coordinates, and degrees of freedom. The student practiced setting up the Lagrangian for the hemispherical bowl problem and deriving the equations of motion. The next session will review spherical coordinates and continue problem-solving.

The Student and Tutor reviewed concepts in statistical mechanics, including microstates, macrostates, phase space, ensembles, entropy, and partition functions. They worked through problems involving lattices and diatomic molecules, focusing on how to specify microstates and calculate partition functions. The student was assigned to review the concepts and problems, with a follow-up session scheduled to continue the discussion.

Sarthak is tutoring Haroon on vectors and related physics concepts in preparation for an exam. They covered scalar vs. vector quantities, dot and cross products, displacement, relative velocity, and began solving a physics problem involving projectile motion. They plan to continue tutoring tomorrow evening, focusing on friction, banking of roads, incline problems, and resilience.

Sarthak tutored Haroon, covering thermodynamics, heat transfer, and mechanics, including diffusion, Brownian motion, specific heat, calorimetry, and the first law of thermodynamics. They worked through numerical problems and discussed the concept of weightlessness in elevators and satellites. They agreed to cover vectors in the next session to help with mechanics problems.