Unit 1
Fundamentals of Dynamics: Reference frames, Inertial frames, Galilean transformations,
Galilean invariance, Review of Newton’s Laws of Motion. Momentum of variable mass
system: motion of rocket. Dynamics of a system of particles. Principle of conservation of
momentum. Impulse. Determination of Centre of Mass of discrete and continuous objects
having cylindrical and spherical symmetry (1-D, 2-D & 3-D).

Unit 2
Work and Energy: Work and Kinetic Energy Theorem. Conservative and nonconservative
forces. Potential Energy. Energy diagram. Stable, unstable and neutral
equilibrium. Force as gradient of potential energy. Work & Potential energy. Work done by
non-conservative forces. Law of conservation of Energy.

Collisions: Elastic (1-D and 2-D) and inelastic collisions. Centre of Mass and Laboratory
frames.

Unit 3
Rotational Dynamics: Angular momentum of a particle and system of particles. Torque.
Principle of conservation of angular momentum. Rotation about a fixed axis. Moment of
inertia, theorem of parallel and perpendicular axes. Determination of moment of inertia of
discrete and continuous objects [1-D, 2-D & 3-D (rectangular, cylindrical and spherical)].
Kinetic energy of rotation. Motion involving both translation and rotation.

Unit 4
Gravitation and Central Force Motion: Law of gravitation. Gravitational potential
energy. Inertial and gravitational mass. Potential and field due to spherical shell and solid
sphere.

Motion of a particle under a central force field: Two-body problem, its reduction to onebody
problem and its solution. Reduction of angular momentum, kinetic energy and total
energy. The energy equation and energy diagram. Kepler’s Laws. Satellite in circular orbit,
Geosynchronous orbits.

Unit 5
Oscillations: Idea of SHM. Differential equation of SHM and its solution. Kinetic energy,
potential energy, total energy and their time-average values. Compound pendulum. Damped
oscillation. Forced oscillations: Transient and steady states, sharpness of resonance and
Quality Factor.

Non-Inertial Systems: Non-inertial frames and fictitious forces. Uniformly rotating frame.
Centrifugal force. Coriolis force and its applications.

Unit 6
Special Theory of Relativity: Outcomes of Michelson-Morley Experiment. Postulates of
Special Theory of Relativity. Lorentz Transformations. Simultaneity, Length contraction,
Time dilation. Relativistic transformation of velocity, acceleration, frequency and wave
number. Mass of relativistic particle. Mass-less Particles. Mass-energy Equivalence.
Relativistic Doppler effect (transverse and longitudinal). Relativistic Kinematics (decay
problems, inelastic collisions and Compton effect). Transformation of Energy and
Momentum.