The learning objective of the course is to provide a complete knowledge of classical mechanics via the following learning achievements:
In particular the course aims at developing the following skills:
The course is worth 6 CFU and will be structured in front lectures (5 CFU) and example classes (1 CFU).
Physical quantities and measure units. The scientific method. Physical quantities and measure units. The International System of Units (SIU). Scientific notation. Dimensionality. Fundamental quantities and derived quantities. Measurement of errors and approximations. Significant figures. Approximation of mathematical functions.
Vector calculus. Scalar quantities and vectors. Invariance and symmetry of systems. Vector calculus: algebra, derivatives and integrals with vectors.
Kinematics. Equations of motion. Linear motion and uniformly accelerated linear motion. Vertical motion. Harmonic oscillator. Damped linear motion. Motion in a plane: velocity and acceleration. Circular and parabolic motion. Motion in the space.
Dynamics of point particles. Newton’s laws. Impulse (step) and momentum. Sum and equilibrium of forces. Examples: weight, friction, viscosity, centripetal force, elastic force and Hook’s law. Inclined plane. Pendulum. Tension. Frames of reference. Relative velocity and acceleration. Inertial frames of reference. Galilean invariance.
Work and energy. Work, power and kinetic energy. Theorem of kinetic energy and examples. Conservative forces and potential energy. Non-conservative forces. Conservation of energy. Force vs potential energy. Angular momentum. Central forces.
Systems of point particles. Systems of n point particles. Internal and external forces. Centre of mass. Conservation of momentum. Conservation of angular momentum. König’s theorem. Kinetic energy theorem.
Rigid body dynamics. Properties of a rigid body. Motion of a rigid body. Continuous distribution of mass, density and position of the body mass. Rigid rotations in three dimensions in an inertial frame of reference. Energy and virtual work of forces. Inertia. Huygens-Steiner’s theorem. Pendulum. Pure rolling. Conservation of energy in the motion of a rigid body. Rolling resistance.
Oscillators and waves. Differential equation of a harmonic oscillator. Equation of motion and solution for simple harmonic oscillator. Mass-spring system: a simple harmonic oscillator. Energy of a simple harmonic oscillator. Sum of harmonic oscillators in one and two dimensions. Damped and driven harmonic oscillators. Resonance.
Fluid mechanics. Fluids. Pressure. Static equilibrium. Archimede’s principle. Internal friction and ideal fluid’s viscosity. Fluid flow: steady and unsteady flow. Flow rate. Bernoulli’s theorem. Torricelli’s theorem. Pascal’s principle. Laminar vs turbulent flow.
Gravity. Central forces. Kepler’s laws. Newton’s law of universal gravitation. Inertia vs gravitational mass. Gravitational fields and gravitational potential energy.