COURSE GOALS: The principle objectives of the course Classical Mechanics 1 are the introduction of fundamental laws and methods of classical mechanics, further development of acquired mathematical skills and their applications to selected physical problems, and the preparation of students for more advanced courses in theoretical physics.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics;
1.2. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena);
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem;
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.3. use mathematical methods to solve standard physics problems;
4. COMMUNICATION SKILLS
4.3. present their own research results at education or scientific meetings;
4.4. use the written and oral English language communication skills that are essential for pursuing a career in physics and education;
5. LEARNING SKILLS
5.3. search for and use professional literature as well as any other sources of relevant information;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the course Classical mechanics 1, students will be able:
* to formulate basic principles of classical mechanics including Newton's determinism, Galilean invariance and the laws of conservation of momentum, angular momentum and energy;
* to analyze the motion of a general mechanical system with one degree of freedom and solve Newton's equation analytically for a number of standard problems;
* to sketch possible trajectories of a particle moving in a central force field and solve Newton's equation analytically for several standard types of central forces, including the Kepler problem;
* to describe the Rutherford's experiment, derive analytical expressions for differential and total cross section and provide physical interpretation of these results;
* to perform the expression for the kinetic energy and angular momentum of the rigid body
* to construct the inertia tensor for several selected examples of rigid bodies (sphere, cube, cylinder, cone, triangle, etc.) and determine the principle axes of an arbitrarily shaped rigid body;
* Introduction and historical development of classical mechanics. Space and time in classical mechanics. Galilean transformations. Newton's formulation of classical mechanics.
* The laws of conservation of momentum, angular momentum and energy. Conservative systems.
* The Newton equation for body motion in 1D potential. Body motion in a medium with resistance in the gravitational field of the Earth.
* Two body problem. Newton equation in spherical coordinates. Motion in central potential and separation of Newton's equation in the radial and angular part.
* Particle moving in an attractive and repulsive Kepler potential.
* Scattering and Rutheford's experiment.
* Rigid body kinematics. Fixed and moving system and the concept of angular velocity. The kinetic energy and tensor of inertial for an arbitrary rigid body. The principle axis of an arbitrary rigid body.
* Rigid body dynamics. Examples: cylinder rolling on a horizontal surface, physical pendulum and heavy symmetric top.
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend classes, participate actively in solving problems and solve homework. Furthermore, students are required to pass two written examinations during the semester.
GRADING AND ASSESSING THE WORK OF STUDENTS:
At the end of the course a written and oral examination is held for students who have successfully completed the requirements of the course.
- Murray R. Spiegel, ''Theory and problems of Theoretical Mechanics'', Schaum's outline series
- Skripta:T. Nikšić, ''Klasicna mehanika1'', online.
- H. Goldstein, C. P. Poole, J. L. Safko (2001), ''Classical Mechanics'' (3rd edition ed.). Addison-wesley.