Mechanics

Dr. Aleksandar Skeparovski, Professor

Dr. Elena Vckova Bebekovska, Assistant

Course content:

• Mathematical introduction: vectors, concept of derivative and integral, differentiation of vectors.

• Kinematics: reference systems, velocity and acceleration, angular quantities, transformation of velocities and accelerations.

• Newton's laws: Newton's first law, inertial reference systems and Galilean transformations, Newton's second and third laws, application of Newton's laws.

• Work and energy: work and kinetic energy, conservative forces and potential energy, law of conservation of mechanical energy, power.

• Momentum: momentum of a material point, law of conservation of momentum, momentum of a force, collisions and center of mass.

• Rotational motion: kinetic energy during rotation, moment of inertia, moment of force, moment of momentum, equation of moments, law of conservation of momentum.

• Gravitation: Kepler's laws, Newton's law of gravity, gravitational potential energy, motion of satellites, gravitational interaction of spherically symmetric bodies.

• Non-inertial reference systems: uniformly accelerated systems, rotating coordinate systems, inertial forces (centrifugal and Coriolis force).

• Mechanics of elastic rigid bodies: static equilibrium and center of gravity; Hooke's law and modulus of elasticity.

• Fundamentals of fluid mechanics: pressure, thrust force – Archimedes' law, equation of continuity, Bernoulli's equation, viscosity and Poiseuille's law.

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