Laws of Motion & Frame of Reference

• Laws of motion

Newton’s first law of motion or law of inertia
Newton’s second law of motion
Newton’s third law of motion

• Conservation of momentum & energy

Law of conservation of linear momentum
Law of conservation of angular momentum
Principle of conservation of energy
Work-energy theorem
Conservative forces

• Co-ordinate frames
• Relative motion
• Inertial and non-inertial frame of reference
• Galilean transformation
• Galilean invariance
• Pseudo or fictitious force
• Centrifugal force
• Transformation of coordinate in a rotating frame of reference
• Transformation of velocity & acceleration in a rotating frame of reference
• Transformation of displacement in a rotating frame
• Uniformly rotating frame of reference and Coriolis force
• Effect of centrifugal and Coriolis forces due to earth’s rotation
• Foucault’s pendulum
• Weightlessness

Gravitational Field and Potential

• Introduction
• Newton’s universal law of gravitation
• Gravitational field and its intensity
• Gravitational potential
• Gravitational potential energy
• Gravitational potential and field due to a spherical shell
• Gravitational potential and field due to a solid sphere
• Laplace’s and Poisson’s equation for gravitational potential
• Gauss’s law for gravity
• Gravitational self energy
• Gravitational self energy of a uniform sphere

Dynamics of the System of Particles

• Centre of mass

Centre of mass of a two particles system
Centre of mass of a system of n-particles
Centre of mass of a solid body

• Centre of mass of regular rigid bodies

Centre of mass of a semi circular disc
Centre of mass of hemispherical rigid body
Centre of mass of a uniform right circular cone
Centre of mass of a triangular plate

• Motion of centre of mass (velocity and acceleration of C.M.)
• Centre of mass frame or C-frame
• Conservation of linear momentum
• Kinetic energy of a system of particles
• Collision of particles

Elastic one dimensional collision or head on elastic collision of two particles
Elastic collision in two or three dimension
Perfectly inelastic collision

• Scattering and scattering cross section
• Scattering of α-particle or proton by heavy nucleus (Rutherford scattering by hard spheres)
• System of variable mass (propulsion of rocket)
• Two particle system (two body problem) and reduced mass
• Applications of reduced mass
• Binary star

Rotational Motion and Rigid Body Dynamics

• Angular momentum and torque
• Law of conservation of angular momentum
• Examples or the applications of conservation of angular momentum

Deduction of Kepler’s second law of planetary motion
The orbit of the planet always lies in a fixed plane
Variation of linear speed of planet in its orbit
The speed of a satellite at apogee and perigee

• Physical meaning of angular momentum
• Angular momentum of system of particles and torque
• Angular momentum of system of particles with respect to C.M.
• Rigid body
• The general motion of a rigid body
• Moment of inertia of a rigid body
• Motion of a rotating rigid body, angular momentum and torque
• Applications of the law of conservation of angular momentum
• Equations of rotational motion
• Newton’s laws of rotational motion
• Comparison of linear and rotational motions
• Degrees of freedom
• Euler’s equation

Motion under a Central Force Field and Kepler’s Law

• Central force
• Equation of motion under central force field
• Energy of motion of particle
• Orbital motion of particle under central force field
• Constants of the elliptical orbit
• Circular orbit and their stability
• Kepler’s laws

Law of area
Law of elliptical orbits
Law of periods

Molecular Rotations and Gyroscopic Motion

• Molecular rotations
• Moment of inertia of a diatomic molecule
• Moment of inertia of a tri-atomic molecule
• Intrinsic spin
• Precession of a symmetric top under the action of external torque
• Gyroscope
• Applications of gyroscope

Elasticity

• Introduction
• Stress

Longitudinal or normal stress
Volume or bulk stress
Tangential or shearing stress
Sonometer

• Strain

Longitudinal or tensile strain
Volumetric Strain
Shear strain or strain of shape

• Hooke’s law
• Elastic limit
• Behaviour of a wire or bar under increasing stress [stress versus strain]
• Elastic behaviour of solids in general

Elastic after effect
Elastic hysteresis
Elastic fatigue

• Different types of elasticity

Young’s modulus (elasticity of length)
Bulk modulus
Modulus of rigidity or shear modulus

• Poisson’s ratio
• Work done in stretching a wire
• Theorems of stress & strain
• Relations between the various elastic constants
• Limiting value of Poisson’s ratio
• Determination of Poisson’s ratio for rubber
• Torsion of a cylinder
• Bending of beams
• Cantilever
• Beam supported at its ends and loaded in the middle
• Applications of bending of beams
• Determination of young’s modulus by bending of a beam

Kinematics of Moving Fluid (Viscosity)

• Introduction
• Streamline and turbulent flow
• Reynold’s number)
• Equation of continuity
• Energy of a liquid
• Euler’s equation of motion for fluidity
• Bernoulli’s theorem
• Applications of Bernoulli’s theorem
• Bernoulli’s Theorem from Euler’s equation of motion for fluidity
• Viscosity
• Coefficient of viscosity
• Flow of liquid through capillaries : Poiseuille’s equation
• Limitations and corrections to Poiseuille’s formula
• Poiseuille’s method of determination of η for a liquid
• Determination of viscosity of given liquid using Ostwald’s viscometer/li>
• Motion of a body in a viscous medium and Stokes’ law
• Measurement of viscosity by rotating cylinder method
• Variation of viscosity with temperature and pressure