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3.4. Classical Mechanics (CME)

Classical Mechanics provides the foundational principles governing the motion of macroscopic objects, from particles to rigid bodies and continuous media. It encompasses Newtonian dynamics, conservation laws, Lagrangian and Hamiltonian formalisms, oscillatory systems, and celestial mechanics.

Knowledge Area (KA)	Core Tier1	Core Tier2
3.4.1 Kinematics and Dynamics of Particles	1	1
3.4.2 Rotational Motion and Angular Momentum	1	1
3.4.3 Elasticity	1	1
3.4.4 Fluids: Hydrostatics, Hydrodynamics, and Viscosity	1	1
3.4.5 Vibrations and Waves	1	1
3.4.6 Transport Phenomena	1	1

3.4.1. CME/Kinematics and Dynamics of Particles  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Mathematical description of motion and the study of forces that cause or modify motion for point particles, forming the basis of mechanical and structural architectural analysis.
Topics:
Core

• Vector description of position, velocity, and acceleration in Cartesian, polar, and spherical coordinates
• Newton's three laws of motion and inertial reference frames
• Formulation and solution of equations of motion for constant and variable forces
• Static and kinetic friction forces, including angle of repose
• Numerical integration of equations of motion for architectural dynamics problems

Learning Outcomes:
Core:

1. Formulate the equations of motion for a particle in one, two, and three dimensions given a force law [Usage]
2. Identify all forces acting on a particle and draw a correct free-body diagram [Familiarity]
3. Calculate the terminal velocity of an object falling through a fluid with drag resistance [Assessment]
4. Implement a numerical algorithm to simulate the dynamics of an architectural mechanical system [Usage]
5. Construct and interpret phase space diagrams for simple architectural oscillatory systems [Assessment]

3.4.2. CME/Rotational Motion and Angular Momentum  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Rotational kinematics and dynamics, torque, moment of inertia, rotational energy, and conservation of angular momentum for architectural machines and structures.
Topics:
Core

• Rotational kinematics: angular displacement, velocity, and acceleration
• Torque: \(\vec{\tau} = \vec{r} \times \vec{F}\) and its computation
• Moment of inertia \(I = \sum m_i r_i^2\) and the parallel axis theorem
• Rotational kinetic energy: \(K_{rot} = \frac{1}{2}I\omega^2\)
• Conservation of angular momentum in architectural machines and rotating structures
• Rolling without slipping dynamics and applications to wheels and shafts

Learning Outcomes:
Core:

1. Calculate torque about a given axis for an architectural power transmission system [Usage]
2. Determine the moment of inertia for machine components such as rods, disks, and shafts [Usage]
3. Apply conservation of angular momentum to analyze speed changes in rotating architectural systems [Assessment]
4. Analyze combined translational and rotational motion in wheeled architectural systems [Assessment]

3.4.3. CME/Elasticity  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Elastic properties of solids under axial, shear, and volumetric load: stress, strain, and scalar elastic moduli.
Topics:
Core

• Definition of stress (force/area) and strain (\(\Delta L/L\))
• Young's modulus and Hooke's law for longitudinal strain: \(\sigma = E\epsilon\)
• Shear modulus (rigidity) and shear strain
• Bulk modulus (compressibility) and volumetric strain
• Elastic limit, plastic region, and fracture point on the stress-strain diagram

Elective

• Elastic energy stored in a deformed material

Learning Outcomes:
Core:

1. Apply the scalar Hooke's law to calculate the deformation of a rod under axial load [Usage]
2. Calculate Young's, shear, or bulk modulus from experimental stress-strain data [Usage]
3. Identify the elastic region, elastic limit, and fracture point on a stress-strain curve [Familiarity]

Elective:

1. Calculate the elastic potential energy stored in a deformed spring or rod [Usage]

3.4.4. CME/Fluids: Hydrostatics, Hydrodynamics, and Viscosity  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Statics and dynamics of incompressible fluids: pressure, buoyancy, the continuity and Bernoulli equations, and an introduction to viscous flow.
Topics:
Core

• Density, pressure, and its variation with depth in a fluid at rest: \(p = p_0 + \rho g h\)
• Pascal's principle and its applications (hydraulic press)
• Archimedes' principle, buoyant force, and flotation
• Pressure measurement with manometers and barometers
• Continuity equation for incompressible flow: \(A_1 v_1 = A_2 v_2\)
• Bernoulli's equation and energy conservation in ideal flow
• Applications: Venturi tube, Torricelli's theorem, Pitot tube

Elective

• Viscosity and Poiseuille's law for laminar flow in pipes
• Reynolds number and the transition to turbulent flow
• Stokes' law for the drag force on a sphere in a viscous fluid

Learning Outcomes:
Core:

1. Calculate the pressure at a point in a fluid at rest given depth and density [Usage]
2. Apply Archimedes' principle to determine whether an object floats, sinks, or remains in equilibrium [Usage]
3. Apply the continuity and Bernoulli equations to solve flow problems in pipes of varying cross-section [Usage]
4. Interpret manometer and barometer readings to determine absolute and gauge pressures [Assessment]

Elective:

1. Apply Poiseuille's law to calculate the flow rate of a viscous fluid in a cylindrical tube [Usage]
2. Estimate the Reynolds number of a flow and predict whether it is laminar or turbulent [Assessment]

3.4.5. CME/Vibrations and Waves  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Simple harmonic motion, damped and forced oscillations, and the propagation, superposition, and resonance of mechanical waves.
Topics:
Core

• Simple harmonic motion (SHM): equation of motion, position, velocity, and acceleration
• Oscillating systems: spring-mass and simple/physical pendulum
• Energy in simple harmonic motion
• Damped and forced oscillations; introduction to resonance
• Transverse and longitudinal waves; propagation speed
• Wave equation and speed of a wave on a taut string: \(v = \sqrt{T/\mu}\)
• Superposition principle and standing waves
• Sound waves, intensity, and sound intensity level (decibels)

Elective

• Doppler effect for sound waves
• Beats and interference of waves of nearby frequencies

Learning Outcomes:
Core:

1. Derive the equation of motion and the period of a spring-mass system and a simple pendulum [Usage]
2. Calculate the kinetic, potential, and total energy of a simple harmonic oscillator at any instant [Usage]
3. Analyze the amplitude response of a forced oscillator near the resonance frequency [Assessment]
4. Calculate the propagation speed of a wave on a string from the tension and linear density [Usage]
5. Determine the frequencies and wavelengths of the normal modes of a standing wave on a fixed string [Usage]
6. Calculate the sound intensity level in decibels from the intensity of a sound wave [Usage]

Elective:

1. Apply the Doppler effect formula for a moving source and/or observer [Usage]

3.4.6. CME/Transport Phenomena  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Introduction to transport phenomena in continuous media: heat conduction and mass diffusion as gradient-driven flux processes.
Topics:
Core

• Heat conduction and Fourier's law: \(\vec{q} = -k\nabla T\)
• Thermal conductivity of materials and thermal resistance in composite walls
• Molecular diffusion and Fick's first law: \(\vec{J} = -D\nabla C\)

Elective

• Analogy between heat, mass, and momentum transport (Prandtl and Schmidt numbers)

Learning Outcomes:
Core:

1. Apply Fourier's law to calculate the heat flux through a plane or composite wall [Usage]
2. Apply Fick's first law to calculate the diffusive flux of a species in a concentration gradient [Usage]

Elective:

1. Identify mathematical analogies between heat, mass, and momentum transport processes [Familiarity]