Applied Physics for Engineering I: Mechanics

Define mechanics as the physics of motion, forces, and interactions, focusing on solid mechanics and engineering applications, including statics, dynamics, and kinematics.

Explore Newtonian mechanics and the force-based formulation, deriving f equals ma and dp/dt for translational and rotational motion, including torque and angular momentum in rigid bodies.

Explore how work transfers energy, how force relates to displacement, and the work-energy theorem for kinetic and potential energy, including gravitational potential energy and conservation of energy.

Explore dynamics and angular momentum, linking torque to angular acceleration, and define angular momentum as the cross product of position and momentum; examine moment of inertia and rotational kinetic energy.

Explore statics and equilibrium in structures by analyzing force and moment balance to keep bodies at rest or moving with constant velocity, ensuring zero net force and zero net moment.

Explore how the Lagrangian formulation uses generalized coordinates to describe motion by the difference between kinetic and potential energy, grounded in the principle of stationary action and Euler-Lagrange equations.

apply the Euler-Lagrange equation to a two-mass pulley, set x1 = x and x2 = l − x, and obtain x'' = (m1 − m2) g /(m1 + m2).

Examine the mechanics of vibrations, including free and forced vibration, resonance, and modal and numerical analysis to identify natural frequencies and assess stability in machines and components.

Study free and forced vibrations, distinguishing natural frequency and damping from external forces, and apply mass and stiffness (via Hooke's law and Young's modulus) to predict resonance and vibration modes.

Explore resonance and damping in engineering systems, where matching external driving frequency to the natural frequency causes amplified vibrations and potential failure, and how damping and models prevent collapse.

Explore stress and strain in materials, including elasticity and Hooke's law, the elastic region, yield and plastic deformation, ultimate strength, fracture, and the role of Young's modulus in design.

Analyze axial loads to reveal elongation or compression and sign of normal stress, and describe shear stress tau and torsional loads via torque, radius, and the polar moment of inertia.

Explore beam bending and deflection analysis under transverse loads, linking bending moment, flexural rigidity, and deflection to design beams by increasing moment of inertia or Young's modulus.

Assess material properties such as stiffness, elastic deformation, yield and ultimate tensile strengths, ductility, and toughness to distinguish elastic and brittle materials and their failure modes.

Explains metallic microstructures, including grains, faces, and defects, and shows how grain size and phase arrangement influence strength, hardness, and ductility through nucleation, boundaries, and heat treatments.

Identify and avoid resonance by keeping natural frequencies away from external vibrations to prevent stress concentrations and fatigue in mechanical components.

Stress concentrations occur at geometric changes like holes or notches, reducing cross sectional area and raising stress; material weaknesses such as voids or microcracks and rounded corners influence failure risk.

Understand how fatigue weakens materials under cyclic loads below tensile strength, initiating microcracks and causing failure in components like aircraft wings; apply s-n curves to predict fatigue life.

Develop a strong understanding of mechanics, both mathematical and applied for industry, and learn thermal fluids and modern physics to prevent and diagnose failures; complete the three-part Udemy specialization certificate.