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Mechanics

A.Y. 2017/2018

Learning objectives

Gli studenti al termine del corso avranno acquisito le conoscenze di base della fisica classica sulle leggi che regolano i moti, le forze, il lavoro e l'energia, la gravitazione, i sistemi di riferimento inerziali e non, la dinamica dei sistemi di punti materiali, il corpo rigido e gli urti. In particolare avranno acquisito la capacità di risolvere problemi che richiedono applicazioni anche non banali di queste leggi.

Expected learning outcomes

Undefined

**Lesson period:**
First semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### CORSO A

Responsible

Lesson period

First semester

**Course syllabus**

Experimental Physics 1

Prof. Marco Bersanelli and Prof. Marcello Fanti

This is the first physics course that students will follow. Its aim is to give to them knowledge of the laws of classical mechanics and to teach them how to apply in simple but significant cases. Effort is also done to teach the students how the laws derive from experimental observations.

Program:

1) Physical quantities, systems of units and dimensional analysis

2) Vector calculus. Sum and difference of vectors. Multiplication of a vector by a scalar. Vector decomposition. Inner (dot) product and vector (cross) product of vectors. Vector as a function of a parameter: vector derivative and integration. Flux of a vector through a surface.

3) Kinematics of a point mass. Velocity. Acceleration. Linear motion: uniform and uniformly accelerated. Motion in the plane: velocity and acceleration in polar coordinates, tangent and normal acceleration. Circular motion. Angular velocity and angular acceleration (including vector notation). Projectile motion. Harmonic motion.

4) Dynamics of a point mass: the three laws of dynamics (Newton's laws of motion). Constant forces, force as a function of speed, position, time. Normal forces. Friction. Momentum. Impulse. Work, power, kinetic energy. Work-kinetic energy theorem. Conservative forces. Potential energy. Conservation of mechanical energy. Calculation of work and potential energy for weight and elastic force. Angular momentum and torques. Central forces and central force motion.

5) Systems of point masses. Centre of mass: properties and motion description. Euler's laws of motion for systems of point masses. Work-kinetic energy theorem. König theorems. Collisions. Ballistic pendulum.

6) Rigid body. Kinematics of rigid bodies. Momentum of inertia. Huygens-Steiner theorem. Dynamics of free and constrained rigid bodies. Rigid bodies rotating around an axis. Physical (compound) pendulum. Roto-translation of a rigid body. Rolling without slipping of spheres and cylinders on a plane. Kinetic energy of translating, rotating, and roto-translating rigid bodies. Work-Kinetic energy theorem and energy conservation for a rigid body.

7) Relative motions. Absolute and relative reference frames. Composition of velocities. Composition of accelerations: Coriolis' theorem. Earth as a relative frame: variation of gravity acceleration with latitude, east deviation of falling objects, Foucault pendulum. Relative dynamics. Apparent forces.

8) Basics of special relativity theory. Crisis of Galilean relativity principle. Lorentz transformations and invariance of physical laws in inertial systems. Transformation of velocities. Lengths contraction and time dilation. Relativistic momentum. Force. Kinetic energy. Rest energy.

9) Universal gravitation. Gravitational force, gravitational field, work of the gravitational force and gravitational potential energy, gravitational potential. Discussion on potential energy curves. Kepler's laws. Gauss theorem and its applications.

10) Basics of fluid dynamics. Pressure, pressure forces, work of pressure forces. Hydrostatic equilibrium and Stevin's law. Archimedes' principle. Fluid motion: stationary regime and flow rate. Ideal fluid. Bernoulli's theorem.

EXAM

Written and oral test.

Prof. Marco Bersanelli and Prof. Marcello Fanti

This is the first physics course that students will follow. Its aim is to give to them knowledge of the laws of classical mechanics and to teach them how to apply in simple but significant cases. Effort is also done to teach the students how the laws derive from experimental observations.

Program:

1) Physical quantities, systems of units and dimensional analysis

2) Vector calculus. Sum and difference of vectors. Multiplication of a vector by a scalar. Vector decomposition. Inner (dot) product and vector (cross) product of vectors. Vector as a function of a parameter: vector derivative and integration. Flux of a vector through a surface.

3) Kinematics of a point mass. Velocity. Acceleration. Linear motion: uniform and uniformly accelerated. Motion in the plane: velocity and acceleration in polar coordinates, tangent and normal acceleration. Circular motion. Angular velocity and angular acceleration (including vector notation). Projectile motion. Harmonic motion.

4) Dynamics of a point mass: the three laws of dynamics (Newton's laws of motion). Constant forces, force as a function of speed, position, time. Normal forces. Friction. Momentum. Impulse. Work, power, kinetic energy. Work-kinetic energy theorem. Conservative forces. Potential energy. Conservation of mechanical energy. Calculation of work and potential energy for weight and elastic force. Angular momentum and torques. Central forces and central force motion.

5) Systems of point masses. Centre of mass: properties and motion description. Euler's laws of motion for systems of point masses. Work-kinetic energy theorem. König theorems. Collisions. Ballistic pendulum.

6) Rigid body. Kinematics of rigid bodies. Momentum of inertia. Huygens-Steiner theorem. Dynamics of free and constrained rigid bodies. Rigid bodies rotating around an axis. Physical (compound) pendulum. Roto-translation of a rigid body. Rolling without slipping of spheres and cylinders on a plane. Kinetic energy of translating, rotating, and roto-translating rigid bodies. Work-Kinetic energy theorem and energy conservation for a rigid body.

7) Relative motions. Absolute and relative reference frames. Composition of velocities. Composition of accelerations: Coriolis' theorem. Earth as a relative frame: variation of gravity acceleration with latitude, east deviation of falling objects, Foucault pendulum. Relative dynamics. Apparent forces.

8) Basics of special relativity theory. Crisis of Galilean relativity principle. Lorentz transformations and invariance of physical laws in inertial systems. Transformation of velocities. Lengths contraction and time dilation. Relativistic momentum. Force. Kinetic energy. Rest energy.

9) Universal gravitation. Gravitational force, gravitational field, work of the gravitational force and gravitational potential energy, gravitational potential. Discussion on potential energy curves. Kepler's laws. Gauss theorem and its applications.

10) Basics of fluid dynamics. Pressure, pressure forces, work of pressure forces. Hydrostatic equilibrium and Stevin's law. Archimedes' principle. Fluid motion: stationary regime and flow rate. Ideal fluid. Bernoulli's theorem.

EXAM

Written and oral test.

FIS/01 - EXPERIMENTAL PHYSICS - University credits: 7

Practicals: 20 hours

Lessons: 40 hours

Lessons: 40 hours

Professors:
Bersanelli Marco Rinaldo Fedele, Bina Matteo

### CORSO B

Responsible

Lesson period

First semester

**Course syllabus**

Experimental Physics 1

Prof. Marco Bersanelli and Prof. Marcello Fanti

This is the first physics course that students will follow. Its aim is to give to them knowledge of the laws of classical mechanics and to teach them how to apply in simple but significant cases. Effort is also done to teach the students how the laws derive from experimental observations.

Program:

1) Physical quantities, systems of units and dimensional analysis

2) Vector calculus. Sum and difference of vectors. Multiplication of a vector by a scalar. Vector decomposition. Inner (dot) product and vector (cross) product of vectors. Vector as a function of a parameter: vector derivative and integration. Flux of a vector through a surface.

3) Kinematics of a point mass. Velocity. Acceleration. Linear motion: uniform and uniformly accelerated. Motion in the plane: velocity and acceleration in polar coordinates, tangent and normal acceleration. Circular motion. Angular velocity and angular acceleration (including vector notation). Projectile motion. Harmonic motion.

4) Dynamics of a point mass: the three laws of dynamics (Newton's laws of motion). Constant forces, force as a function of speed, position, time. Normal forces. Friction. Momentum. Impulse. Work, power, kinetic energy. Work-kinetic energy theorem. Conservative forces. Potential energy. Conservation of mechanical energy. Calculation of work and potential energy for weight and elastic force. Angular momentum and torques. Central forces and central force motion.

5) Systems of point masses. Centre of mass: properties and motion description. Euler's laws of motion for systems of point masses. Work-kinetic energy theorem. König theorems. Collisions. Ballistic pendulum.

6) Rigid body. Kinematics of rigid bodies. Momentum of inertia. Huygens-Steiner theorem. Dynamics of free and constrained rigid bodies. Rigid bodies rotating around an axis. Physical (compound) pendulum. Roto-translation of a rigid body. Rolling without slipping of spheres and cylinders on a plane. Kinetic energy of translating, rotating, and roto-translating rigid bodies. Work-Kinetic energy theorem and energy conservation for a rigid body.

7) Relative motions. Absolute and relative reference frames. Composition of velocities. Composition of accelerations: Coriolis' theorem. Earth as a relative frame: variation of gravity acceleration with latitude, east deviation of falling objects, Foucault pendulum. Relative dynamics. Apparent forces.

8) Basics of special relativity theory. Crisis of Galilean relativity principle. Lorentz transformations and invariance of physical laws in inertial systems. Transformation of velocities. Lengths contraction and time dilation. Relativistic momentum. Force. Kinetic energy. Rest energy.

9) Universal gravitation. Gravitational force, gravitational field, work of the gravitational force and gravitational potential energy, gravitational potential. Discussion on potential energy curves. Kepler's laws. Gauss theorem and its applications.

10) Basics of fluid dynamics. Pressure, pressure forces, work of pressure forces. Hydrostatic equilibrium and Stevin's law. Archimedes' principle. Fluid motion: stationary regime and flow rate. Ideal fluid. Bernoulli's theorem.

EXAM

Written and oral test.

Prof. Marco Bersanelli and Prof. Marcello Fanti

This is the first physics course that students will follow. Its aim is to give to them knowledge of the laws of classical mechanics and to teach them how to apply in simple but significant cases. Effort is also done to teach the students how the laws derive from experimental observations.

Program:

1) Physical quantities, systems of units and dimensional analysis

2) Vector calculus. Sum and difference of vectors. Multiplication of a vector by a scalar. Vector decomposition. Inner (dot) product and vector (cross) product of vectors. Vector as a function of a parameter: vector derivative and integration. Flux of a vector through a surface.

3) Kinematics of a point mass. Velocity. Acceleration. Linear motion: uniform and uniformly accelerated. Motion in the plane: velocity and acceleration in polar coordinates, tangent and normal acceleration. Circular motion. Angular velocity and angular acceleration (including vector notation). Projectile motion. Harmonic motion.

4) Dynamics of a point mass: the three laws of dynamics (Newton's laws of motion). Constant forces, force as a function of speed, position, time. Normal forces. Friction. Momentum. Impulse. Work, power, kinetic energy. Work-kinetic energy theorem. Conservative forces. Potential energy. Conservation of mechanical energy. Calculation of work and potential energy for weight and elastic force. Angular momentum and torques. Central forces and central force motion.

5) Systems of point masses. Centre of mass: properties and motion description. Euler's laws of motion for systems of point masses. Work-kinetic energy theorem. König theorems. Collisions. Ballistic pendulum.

6) Rigid body. Kinematics of rigid bodies. Momentum of inertia. Huygens-Steiner theorem. Dynamics of free and constrained rigid bodies. Rigid bodies rotating around an axis. Physical (compound) pendulum. Roto-translation of a rigid body. Rolling without slipping of spheres and cylinders on a plane. Kinetic energy of translating, rotating, and roto-translating rigid bodies. Work-Kinetic energy theorem and energy conservation for a rigid body.

7) Relative motions. Absolute and relative reference frames. Composition of velocities. Composition of accelerations: Coriolis' theorem. Earth as a relative frame: variation of gravity acceleration with latitude, east deviation of falling objects, Foucault pendulum. Relative dynamics. Apparent forces.

8) Basics of special relativity theory. Crisis of Galilean relativity principle. Lorentz transformations and invariance of physical laws in inertial systems. Transformation of velocities. Lengths contraction and time dilation. Relativistic momentum. Force. Kinetic energy. Rest energy.

9) Universal gravitation. Gravitational force, gravitational field, work of the gravitational force and gravitational potential energy, gravitational potential. Discussion on potential energy curves. Kepler's laws. Gauss theorem and its applications.

10) Basics of fluid dynamics. Pressure, pressure forces, work of pressure forces. Hydrostatic equilibrium and Stevin's law. Archimedes' principle. Fluid motion: stationary regime and flow rate. Ideal fluid. Bernoulli's theorem.

EXAM

Written and oral test.

FIS/01 - EXPERIMENTAL PHYSICS - University credits: 7

Practicals: 20 hours

Lessons: 40 hours

Lessons: 40 hours

Professors:
Bernardoni Vera, Fanti Marcello