PAPER A TH: 30, PRACTICAL: 15(Only one Practical with Both Papers A and B)
Paper-A
{Mechanics}
Main Topics
Vector Operations:
Vector in 3 dimensions
(Introduction, Direction of cosines, Spherical polar coordinates, Applications)
Vector Derivatives and
Operations
(Divergence and curl of a vector, Gradient of a scalar)
Gradient, Divergence
And curl of a vector
(Physical applications of each types, Divergence and flux of a vector field, Curl and line integral {Mutal Relation}
Divergence Theorem
(Derivation, Physical importance and applications to specific cases, converting from differential to integral forms)
Stokes Theorem
(Derivation, Physical importance and applications to specific cases, converting from differential to integral forms)
Particle Dynamics
Advanced applications
Of Newton’s Law
(Electrical forces, Microscopic basis of this force)
Dynamic of uniform
Motion
(Conical pendulum, the rotor, Circular the banked curve)
Equation of motion
(Deriving kinematics questions X {V}, V {T} using integrations, Constant and non constant, Forces and special examples)
Time dependent forces
(Obtaining X {T}, V {T} for this case using integration method)
Effect of drag forces
On motion
(Applying Newton’s law to obtain V {T} for the case of motion with time dependent drag {Viscous} forces, Terminal velocity, Projectile motion / air resistance)
Non inertial frames
And pseudo forces
(Qualitative discussion to develop understanding, Calculation of pseudo forces for simple cases {linearly accelerated references frame}, Centrifugal forces as an example of pseudo forces, Carioles forces)
Limitations of Newton’s
Law discussion
Work and Energy
Work done by a constant
Forces, Work done by a
Variable force {1 Dimensional}
(Essentially a review of grade-XII concepts use of integration technique to calculate work done, {e.g. in vibration of a spring obeying Hooke’s law}
Work done by a variable
{2 Dimensional cases}
(Obtaining general expression force and applying to simple cases e.g. pulling a mass at the end of a fixed sting against gravity)
Work energy theorem.
General proof of work
Energy theorem
(Qualitative review of work energy theorem, Derivation using integral calculus, Basic formula, Applications)
Power
Reference frame
(Energy changes with respect to observers in different inertial frames)
Conservation of energy
Conservative, None
Conservative forces
(Definition of either type of force & examples, Work done in a closed path)
(1-D conservative system, Force as the gradient of potential energy, Application to the case a spring and force of gravity)
1 dimensional
Conservative system
(Obtaining velocity in the terms of U and E, Stable, Unstable and neutral equilibrium, Analytic solution for X {T})
2, 3 dimensional
Conservative system
(Change in P.E, for motion in 3-d, Force as the gradient of the potentials, Work done in 2, 3dimensional motion)
Conservation of energy
In a system of particles
(Law of conservation of total energy of an isolated system)
System of Particles
Two particle systems
And generalization to
Many particle systems
(Centre of mass, its position velocity and equation of motion)
Centre of mass of
Solid objects
(Calculation of centre of mass of solid objects using integral calculus, Calculating C.M of
1. Uniform rod
2. Cylinder
3. Sphere
Momentum changes
In a system of variables
Mass
(Derivation of basic equations, Application to motion of a racket {Determination of its mass as a function of time})
Collision
Elastic collision:
Conservation of
Momentum during collision
(a) One dimension
(b) Two dimension {oblique collision}
Inelastic collision,
Collision in centre
Of mass reference frame
(One and two dimensions, Simple application, Obtaining velocities in C.M frame)
Rotational Dynamic
Overview of rotational
Dynamics
(Relation ship between linear & angular variables, Scalar vector form, Kinetic energy of rotation, Moment of inertia)
Parallel axis theorem
(Prove and illustration, Apply simple mass)
Determination of moment
Of inertia of various shapes,
Rotational dynamic of rigid
Bodies
(Equation of rotational motion and effects of application of torques)
Combine rotational
And transnational motion
(Rolling without slipping)
Angular Momentum
Angular velocity
(Definition, Conversion of angular momentum, Effect of torque)
Stability of spinning
Objects
(Discussion with example)
The spinning top
(Effects of torque on the angular momentum, Processional motion)
Gravitation
Review of basic concepts
Of gravitation, Gravitational
Effect of a spherical mass
Distribution
(Mathematical treatment)
Gravitational potential
Energy
(Develop using integration techniques, Calculation of escape velocity)
Gravitational field &
Potential
(Develop the idea of field of force)
Universal gravitational
Law
(Motion of planets and Keplers law {Derivation & Explanation} Motion of satellites, Energy considerations in planetary and satellite motion, Qualitative discussion on application of gravitational law to the galaxy)
Bulk Properties of
Matters
Elastic properties of matter
(Physical basis of elasticity tension, Compression & shearing, elastic modulus, Elastic limit)
Fluid Statics
(Variation of pressure in fluid at rest and with height in the atmosphere)
Surface tension
(Physical basis, Role in formation of drop and bubbles)
Fluid Dynamics
(General concept of fluid flow streamline and the torque of continuity)
Bernoulli’s Equation
(Derivation and some applications such as dynamic lift thrust on a rocket)
Viscosity
(Physical basis, obtaining the coefficient of viscosity, Practical example of viscosity, Fluid flow through a cylindrical pipe {poisenille’s law})
Special Theory of Relativity
Trouble with classical
Mechanics
(Qualitative discussion of the inadequacy or paradoxes in classical ideas of time, Length, and velocity)
Postulates of relativity
(Statements and discussion)
The Lorentz transformation
Inverse transformation
(Derivation, Assumption on which derived, Application of the same transformation of velocities)
Consequences of Lorentz
Transformation
(Relativity of time, Relativity of length)
Relativity momentum
(Derivation)
Relativistic energy
(Derive E=mc2), {E=mc Square}
Posted by: Wasim Javed
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