This is a calculus course covering the basic laws and phenomena
in Mechanics, Thermodynamics, Waves and Optics.
MECHANICS (16 lectures)
Scalars & Vectors
Scalar and vector products. Vectors and their components.
Unit vectors. Vector algebra in terms of their components.
Vector treatment of motion
Position vector and particle trajectory. Average and instantaneous
acceleration. Application to uniform circular motion.
Derivation of a =-w*w*r.Relative
velocity.
Work and Kinetic Energy
General definition of work. Work done by a variable force. One-dimensional
analysis. Interpretation of work as area under graph of F vs. x.
Proof of Work-Kinetic Energy Theorem.
Conservation of Energy
Conservative forces. General definition of potential energy and
examples of its calculation. Mechanical energy.
Proof of conservation of mechanical energy. Non-conservative forces.
Conservation of total energy.
System of Particles
Centre of mass for systems of particles and extended objects.
Newton’s Second Law for systems of particles and extended
objects and consequences. Proof of conservation of linear momentum.
Rotation
Description of rotation using 2 , w
and 'alpha' . Kinematic equations. Kinematic energy of rotation.
Rotational inertia and its calculation for some symmetrical objects.
Parallel and Perpendicular Axes Theorem. Torque t
= r * F and t =I*w.
Work and torque.
Rolling
Definition of rolling. Rolling as a combination of rotation and
translation. Rolling as pure rotation about an instantaneous axis.
Role of friction in rolling. Kinetics and dynamics of rolling.
Definition of angular momentum.
Newton’s Second Law in angular form. Angular momentum for
a system of particles. Conservation of angular momentum and its
application.
Simple Harmonic Motion
Equation of (linear) SHM in differential form and solution as x
= A sin (w t - 2
).
Definition of angular SHM in terms of torque and angular displacement.
Differential equation of motion and its solution. Examples such
as physical pendulum (and limiting case of simple pendulum) and
suspended oscillating disc.
WAVES & OPTICS (12 lectures)
Waves on a String
Transverse and longitudinal waves. The wave equation.
Phase velocity. The sine wave. Power transmission. Superposition
principle. Interference. Standing waves and resonance.
Sound Waves
Wave speed (without derivation). Displacement and pressure waves.
Beats. Doppler effect for sound waves.
Optics
Huygens’ principle (e.g. in refraction). The electromag-netic
wave.
Coherence. Young’s experiment. Intensity in double slit interference.
Thin film interference (including wedge films and Newton’s
rings).
The phasor method. Single slit diffraction. The diffraction grating.
HEAT & THERMODYNAMICS (8 lectures) Temperature, Heat and the
First Law Measuring temperature. Constant volume gas thermometer.
Ideal gas temperature. Measurement of thermodynamic temperature.
Absorption of heat by solids and liquids. Molar specific heat. Heat
and work. Calculation of work done by an ideal gas at constant temperature.
Differential form of First Law of Thermodynamics and application
to selected cases.
Kinetic Theory of Gases
RMS speed, pressure, translational kinetic energy and temperature.
Adiabatic equation of an ideal gas.
Entropy and the Second Law
Entropy and the Second Law of Thermodynamics. Heat engines and refrigerators.
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