This is a pre-calculus course covering fundamental
topics in Mechanics and Heat.
Content: MECHANICS (24 lectures)
Physical Quantities & Units
Physical quantities and their units with mass, length, time and
temperature as fundamental (base) quantities. The nature of physical
quantities: scalars and vectors, components of a vector, addition
and subtraction of vectors by means of components.
Kinematics in One Dimension
Definitions of displacement, speed (average and instantaneous),
velocity (average and instantaneous), acceleration (average and
instantaneous). Displacement-time and velocity-time graphs. Graphical
interpretation of velocity and acceleration. Distance travelled
as area under the velocity-time graph. Derivation of kinematic equations
for constant acceleration and their application to solving problems.
Projectile Motion
Introduction to projectile motion as a combination of two one-dimensional
motions.
Derivation of range, maximum height and time of flight.
Derivation of the equation for the parabolic path.
Application of the equations for projectile motion.
Forces & Newton’s Laws of Motion
Concepts of force, mass and inertia. Statement of Newton’s
laws.
Vector nature of Newton’s second law of motion ( 3 Fx
= max , 3 Fy =may ).
Types of forces: Static and kinetic frictional forces.
Tension.
Gravitational forces.
Newton’s law of gravitation.
Moment of a force.
Equilibrium and conditions for equilibrium. Forces on an object
immersed in a fluid. Pressure and upthrust.
Archimedes’ principle and its derivation using a cubical object.
Simple battery hydrometer.
Viscosity. Statement of Stokes’ law and the concept of terminal
velocity.
Dynamics of Uniform Circular Motion
Introduction to the concept of centripetal acceleration and force.
Centripetal force and motion around a curve. Satellites in circular
orbits.
Work and Energy
Concepts of work and power.
Kinetic and potential energies. Work-Energy theorem. Definition
of conservative force. The principle of conservation of mechanical
energy. Concepts of energy conversion and applications with special
reference to renewable energy sources such as solar, wind, geothermal
and wave.
Impulse and Momentum
Definition of impulse and linear momentum.
Impulse-Momentum theorem.
The principle of conservation of linear momentum including the
derivation using the impulse-momentum theorem.
Application to collisions.
Simple Harmonic Motion
Introduction to Hooke’s law and definition of simple harmonic
motion.
Treatment of light spring-mass system as simple harmonic oscillator.
The displacement-time graph for SHM and the application of x =A
cos(w t) or x =A
sin(w t) to interpret the results. Expressions for velocity, acceleration
and period for SHM.
Energy considerations and conservation for SHM.
The simple pendulum.
HEAT (12 lectures)
Temperature and thermometers.
Thermal equilibrium and the Zeroth law of thermo-dynamics.
Thermal expansion.
The gas laws and absolute temperature. The ideal gas law. The ideal
gas law in terms of molecules. Avogadro’s number.
Kinetic theory.
Real gases and changes of phase.
Vapour pressure and humidity.
Heat and Internal Energy, specific heat capacity.
Calorimetry.
Heat Transfer : Conduction, convection and radiation.
First Law of Thermodynamics, first law applied to simple processes including isobaric and isothermal processes
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