Mechanics
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 02MECH | Z | 4 | 4+2 | Czech |
- Relations:
- The course 02MECHZ can be graded only after the course 02MECH has been successfully completed.
- In order to register for the course 02ELMA, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 02MECH.
- Course guarantor:
- David Břeň
- Lecturer:
- David Břeň
- Tutor:
- David Břeň, Antonín Hoskovec, Magdalena Parýzková, Filip Petrásek, Šárka Salačová, Josef Schmidt, Stanislav Skoupý, Rudolf Šmolka, Vojtěch Teska, Iskender Yalcinkaya
- Supervisor:
- Department of Physics
- Synopsis:
-
Introduction to physics, physical quantities and units. Kinematics of a particle, basic types of motion and their superposition. Dynamics of a particle, solving equations of motion for one-dimensional motion, motion in a central force field, forces in non-inertial reference frames. Mechanics of a system of particles, two-body problems, particle collisions. Mechanics of a rigid body, rotation.
- Requirements:
-
Knowledge of high school mathematics and physics is required. Basic calculus (differentiation and integration) and basic trigonometry would be useful but are not necessary.
- Syllabus of lectures:
-
1. Mathematical preliminaries: Scalars, scalar functions, cartesian and polar coordinates, derivatives, integrals, introduction to first- and second-order homogenous differential equations, vectors, vector operations.
2. Kinematics: Reference frames, position, displacement, velocity, acceleration, speed, average speed, momentum, basic types of motion and their superposition.
3. Dynamics: Inertial and non-inertial reference frames, Newton's laws of motion, equation of motion for a particle under a constant force, inclined plane, tension, drag force, friction, freefall and terminal speed, projectile motion.
4. Rotation: Angular velocity, torque, angular momentum, rotational inertia of a system of particles, Newton's 2nd law in rotational form, uniform circular motion.
5. Conservation theorems: Conservation of linear and angular momentum, work and kinetic energy, conservative forces and potential energy, conservation of total energy, total energy as an equation of motion, equilibrium, impulse, power.
6. Small oscillations: Simple harmonic oscillator, simple pendulum, phase diagrams for the oscillative behavior, damped oscillations, driven oscillations, resonance.
7. Central force motion: Definition of central force, equations of motion for central force problem, orbits, centrifugal energy, effective potential, two-body problem, planetary motion, Kepler's laws.
8. Dynamics of system of particles: Center of mass, reconsideration of basic mechanical quantities, dynamics and conservation laws for system of particles, elastic and inelastic collisions.
9. Motion in a non-inertial reference frame: Centrifugal and Coriolis forces, motion relative to the Earth, oblateness of Earth, cyclonic motion.
10. Dynamics of rigid bodies: Yo-yo problem, physical pendulum, inertia tensor, Euler's equations, force-free motion of a symmetric top.
- Syllabus of tutorials:
-
Practice problems on the covered topics corresponding to the lecture syllabus above.
- Study Objective:
-
Learning the basics of mechanics, and solving simple equations of motion.
- Study materials:
-
Key references:
[1] D. Morin: Introduction to Classical Mechanics: With Problems and Solutions, Cambridge University Press, 2008
[2] J. R. Taylor: Classical Mechanics, University Science Books, 2005
[3] Thornton, S. T., Marion, J. B., - Classical Dynamics of Particles and Systems, 3rd Edition, Brooks/Cole, 2003.
[4] Halliday, D., Resnick, R., Walker, J., Fundamentals of Physics, 10th Edition, Wiley, 2013.
- Note:
-
Full syllabus: https://people.fjfi.cvut.cz/yakcuisk/pdf/mechanics-syllabus.pdf
- Time-table for winter semester 2024/2025:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri - Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Fyzikální inženýrství - Počítačová fyzika (PS)
- Aplikovaná algebra a analýza (compulsory course in the program)
- Aplikované matematicko-stochastické metody (compulsory course in the program)
- Jaderné inženýrství - Aplikovaná fyzika ionizujícího záření (PS)
- Fyzikální inženýrství - Fyzikální inženýrství materiálů (PS)
- Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (PS)
- Fyzikální inženýrství - Inženýrství pevných látek (PS)
- Jaderná a částicová fyzika (compulsory course in the program)
- Jaderná chemie (compulsory course in the program)
- Jaderné inženýrství - Jaderné reaktory (PS)
- Fyzikální inženýrství - Laserová technika a fotonika (PS)
- Matematické inženýrství - Matematická fyzika (PS)
- Matematické inženýrství - Matematická informatika (PS)
- Matematické inženýrství - Matematické modelování (PS)
- Kvantové technologie (compulsory course in the program)
- Radiologická technika (compulsory course in the program)
- jaderné inženýrství - Radioaktivita v životním prostředí (PS)
- Vyřazování jaderných zařízení z provozu (compulsory course in the program)
- Physical Engineering - Computational physics (PS)
- Quantum Technologies (compulsory course in the program)
- Nuclear and Particle Physics (compulsory course in the program)
- Physical Engineering - Physical Engineering od Materials (PS)
- Mathematical Engineering - Mathematical Physics (PS)
- Physical Engineering - Plasma Physics and Thermonuclear Fusion (PS)