5.1. Theoretical topics. The theoretical contents that will be studied during this Course are grouped in nine chapters, sectioned as given in what follows. The approximate number of basics lecture hours dedicated to each chapter is also indicated.
Chapter 1. Introduction: units; motion along a straight line; vector calculus. [4h]
1. Dimensions of the physical magnitudes; systems of units.
2. Straight-line motion: position, velocity and acceleration; displacement travelled.
3. Vector calculus: vectors, vector operations; scalar product, vector product.
Chapter 2. Motion in space. [3h]
1. Reference systems; position vector and coordinates of a point.
2. Motion in space: displacement, velocity, acceleration; intrinsic components of acceleration.
3. Motion with constant acceleration.
4. Circular motion; angular description: angular velocity, angular acceleration.
Chapter 3. Newton’s laws. Applications. [4h]
1. Forces; principle of superposition.
2. Newton’s laws: law of inertia; fundamental law of Dynamics; law of action-reaction.
3. Applications: equations of equilibrium and motion.
4. Important forces: weight, elastic force on a spring, normal reaction on a surface or a curve, tension on a string, friction forces, gravitational forces, electric forces, molecular forces.
Chapter 4. Work and energy. [4h]
1. Work done by a constant force in a straight-line displacement; properties. Power.
2. Kinetic energy theorem.
3. Generalization: work done by a variable force in a straight-line displacement; work done by a force during a displacement along a curved path. Work-energy theorem.
4. Conservative forces, potential energy; important examples.
5. Law of conservation of mechanical energy.
6. Energy diagrams for the straight-line motion.
Chapter 5. Systems of particles. [4h]
1. Systems of particles. External forces, internal forces.
2. Linear momentum; law of conservation.
3. Torque with regards to a point.
4. Angular momentum with regards to point; law of conservation.
5. Centre of mass; equation of motion of the CDM.
5. Kinetic energy; translational kinetic energy and internal kinetic energy.
7. Conservation of the total energy. External energy. Internal energy.
8. Two-body collisions.
Chapter 6. Dynamics of rotational motion. [3h]
1. The rigid body. Motion of a rigid body: translation, rotation.
2. Rotational motion about a fixed axis; rotational kinetic energy.
3. Angular momentum of the rigid body; equation of rotation.
4. Properties of the moment of inertia.
5. Combined translation and rotation.
Chapter 7. Oscillations. [5h]
1. Oscillatory motion; general features.
2. Simple harmonic motion; energy and force in a SHM.
3. Examples of mechanical oscillators: elastic oscillators, penduli.
4. Molecular vibrations.
5. Damped oscillations.
6. Forced oscillations; resonance.
Chapter 8. Motion of a fluid. [5h]
1. Fluids; model of a continuum.
2. Forces in a fluid; pressure.
3. Fluid statics; consequences and applications.
4. Motion of a fluid. Conservation of mass: the continuity equation; conservation of energy: Bernoulli’s law.
5. Applications.
6. Viscosity. Turbulence.
Chapter 9. Waves. [4h]
1. Mechanical waves; transverse and longitudinal waves.
2. Harmonic waves; energy of a harmonic wave.
3. The wave equation; superposition of waves.
4. Examples of mechanical waves: waves on a string, Sound.
5. Wave interference.
6. Standing waves.
5.2. Laboratory session topics. Three two-hour sessions will take place in the laboratory.
Session 1. Uncertainties in experimental measurements. Calculate the volumes of certain bodies by taking measurements via the Vernier caliper.
Session 2. Elastic force on a spring. Hooke’s law.
Session 3. Wave interference. Standing waves on a string.