**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.

### Course Curriculum

FUNDAMENTAL OF DYNAMICS | |||

Introduction to Mechanics | 01:02:00 | ||

Normal Reaction | FREE | 00:36:00 | |

Pseudo Forces | 01:01:00 | ||

Tension | 00:35:00 | ||

Friction | 00:51:00 | ||

Law of Conservation of Linear Momentum | 00:47:00 | ||

Centre of Mass | 00:43:00 | ||

Variable Mass Systems | 00:25:00 | ||

NON-INERTIAL SYSTEMS | |||

Uniformly Rotating Frame | 00:57:00 | ||

Circular Motion | FREE | 01:43:00 | |

Coriolis Force | 00:27:00 | ||

WORK AND ENERGY | |||

Law of Conservation of Energy | 00:39:00 | ||

COLLISION | |||

Collision | 01:35:00 | ||

Collision in CM Frame | 00:36:00 | ||

OSCILLATIONS | |||

Simple Harmonic Motion | 00:43:00 | ||

Lissajous Figures | 00:39:00 | ||

Damped Oscillation | 00:33:00 | ||

Forced Oscillation | 00:48:00 | ||

ROTATIONAL DYNAMICS | |||

Rotation about Fixed Axis | 01:48:00 | ||

Translation + Rotation | FREE | 01:07:00 | |

Angular Momentum | 01:25:00 | ||

Moment of Inertia Tensor | 00:48:00 | ||

MOTION OF PARTICLE UNDER CENTRAL FORCE FIELD | |||

Equivalent One Body Problem | 00:49:00 | ||

Conservation laws in Central Force Motion | FREE | 00:37:00 | |

Trajectory of Particle Undergoing Central Force Motion | 00:43:00 | ||

Types of Central Force Motion | 02:19:00 | ||

Problems on Central Forces | 01:44:00 | ||

GRAVITATION AND CENTRAL FORCE SYSTEM | |||

Gravitation | 00:25:00 | ||

Gravitational Field | 01:42:00 | ||

Gravitational Potential | 00:52:00 | ||

Gravitational Potential Energy | 01:41:00 | ||

SPECIAL THEORY OF RELATIVITY | |||

Einstein postulates | 00:25:00 | ||

Time Dilation and Length Contraction | 00:34:00 | ||

Simultanity and Lorentz Transformation | 00:25:00 | ||

Problems on Relativity | 00:54:00 | ||

Mass and Energy | 00:37:00 |

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