Fundamentals of Physics I 1100-1Ind03

The aim is to present and reinforce basic knowledge within th escope of relativistic mechanics, nonrelativistic gravity, dynamics of discrete and continous systems.

The course consists of lectures with demonstations and exercises on the following topics:

1. Interrelation of geometry and physics. Relativity of space. Spacetime. Material point. Events. Worldline. Free body. Galileo's principle of inertia. Clocks. Position and time. Inertial frame. Free body motion.
2. 2 and 3 inertial frames. Galileo's principle of inertia and its consequences. Composition of velocities. Three possibilities of spacetime geometry: Euclid, Galileo, Einstein. Fizeau experiment in moving water. Minkowski not Galileo! ''Relativistic'' and ''nonrelativistic'' regime.
3. Consequences of the new geometry. Light speed constancy. Twin paradox. Lorentz contraction. Magnetic attraction of currents.
4. Description of ''glueing'' and decay of bodies in Galilean geometry.
Mass. Momentum. Collisions. Conservation of momentum and mass. Where is energy?
5. Description of ''glueing'' and decay of bodies in Minkowskian geometry. Mass. Energy and momentum. Mass defect. Internal energy. Elastin and inelastic collisions.
6. Rocket. Motion of bodies in rarefied medium. Force as the velocity of momentum transfer. Equation F=dp/dt as a definition!
7. Gas in a vessel with unmovable piston. Pressure. Piston motion. Adiabatic regime. Change of piston momentum as a function of position. Force and potential energy.
8. Newton's equations. Determinism.
9. One-dimensional equation of motion. Acceleration. Uniformly accelerated motion. Friction and resistance forces in media. Force proportional to the displacement. Oscillating motion. Oscillator with external force. Damped force. Resonance.
10. Relativistic motion in a constant electric field. ''Longitudinal'' mass.
11. Motion in space. Vectors. Lorentz force. Bainbridge spectrograph. Cyclotron. ''Transversal'' mass. Synchrotron.
12. Description of motion in noninertial frame. Linear acceleration. Uniform rotation. Centripetal force, Coriolis force.
13. Gravity. Its relation to inertial forces. Identity of ''gravitational'' and ''inertial'' masses. Eötvös experiment. Throws.
14. Constraints. Mathematical pendulum. Foucault's pendulum.
15. Law of universal gravitation. Motion in central field. Kepler's laws.
16. Rutherford scattering.
17. Two-body problem. Center-of-mass frame. Tidal forces. Moon-Earth distance. Limited three-body problem. Lagrange points.
18. Coupled oscillators. Superposition of vibrations. Vibrations of many degrees of freedom systems. Eigenmodes. Continuous medium limit.
19. Mechanical waves. Longitudinal and transversal waves. Phase and group velocities. Reflection and refraction of waves. Fourier analysis.
20. Acoustics. Speed of sound. Sound sources. Musical instruments. Doppler's effect.
21. Conservation of angular momentum for many body systems. Rigid body. Moment of inertia. Statics.
22. Stresses in rigid bodies. Displacements in rigid bodies. Hooke's law. Elastic constants.
23. Rotations around moving axes. Angular velocity. Inertia tensor. Properties of gyroscopes.
24. Statics of liquids and gases. Dynamics of liquids and gases. Bernoulli equation. Viscosity.