Vector algebra and dimensional methods.
Force and moment of force.
Systems of forces; couples, equipollent force systems.
Centre of mass, systems of particles, rigid bodies, compound bodies.
Equilibrium, conditions for equilibrium, 2D and 3D, friction.
Kinematics of particles, components of force and acceleration.
Inertial systems.
Newton’s laws for a particle.
Work and energy; power and kinetic energy, conservative systems, energy conservation.
Elements about particle systems.
The moment equation.
Rotation around a fixed axis.
Central motion.
Harmonic linear oscillations in one dimension, free and forced, damped and undamped.
After passing the course the students should be able to: Define the basic concepts and quantities in mechanics and explain how they are related, e.g. velocity, acceleration, mass, time, force, and moment of force. Formulate the laws of motion and derive the connections between them, e.g. Newton’s laws for particles, inertial systems, laws about equilibrium of rigid bodies. Identify and define typical systems of forces and a manifold of more abstract mechanical quantities (center of mass, momentum, angular momentum, resultant force, impulse, angular impulse, work, kinetic and potential energy, conservative and non-conservative forces). Discuss central mechanical phenomena (such as free fall, free damped and undamped harmonic oscillation, forced oscillation, resonance, uniform circular motion, elastic and completely inelastic impact, etc). Prove abstract energy and momentum laws starting from Newton’s laws. Analyze given systems of forces, and simplify them as far as possible. Analyze given motions with suitable choice of coordinate systems (inertial systems). Calculate forces and positions of equilibrium. Starting from Newton’s laws and kinematic and geometric relationships put down mathematical models for different types of particle motions and make calculations of this motion. Plan, search for information, perform, and report in written and oral form a group project related to the contents of the course.
