Mechanical Engineering 101: Forces and Moments ( mechanics )

Define force in classical mechanics through Newton's laws, connect force to mass and acceleration with F=ma, and explain diverse force types and units.

Represent forces as vectors with basis vectors i, j, k and components fx, fy, fz, and measure forces with spring scales, force transducers, or load cells.

Explore forces laws across gravity, springs, electrostatic and electromagnetic forces, hydrostatic, and aero- and hydro-dynamic lift and drag, using Newton’s law to relate mass, distance, and gravity.

Explore electrostatic and electromagnetic forces in engineering design. Apply Coulomb's law to charged particles, permittivity, and forces between parallel plates, and see applications in MEMS and electric motors.

Compute hydrostatic pressure and buoyancy forces in stationary fluids; pressure increases with depth, and Archimedes’ principle yields buoyant force equal to weight of displaced fluid, directed perpendicular to surface.

Explore aerodynamic lift and drag from unsymmetrical flow or spin, and how drag arises from friction and pressure, with CL and CD depending on shape and angle of attack.

Explore how drag and lift arise from fluid flow around objects, and how shape, orientation, asymmetry, viscosity, pressure, and speed define the coefficients CL and CD for airfoils and vehicles.

Compute force vectors by substituting V1, V2, V3 with their values, perform the algebra, and determine the resulting components i and j.

Explore force interactions with labeled drawings: action and reaction between objects, magnet repulsion and attraction at a distance, Venus and a satellite, and ball and hand connected by a wire.

Moment is the tendency of a force to rotate an object about a point, illustrated by a wrench; compute it from the force vector, the position vector, via cross product.

Calculate the moments of a uniform beam under weight W about points A and B using vector cross products, with center of gravity at midpoint and F = -W j.

Explore how wind load and weight acting at the center of gravity determine the position vector r, sum the force resultant, and compute the moment Mb about point B.

this example analyzes moments on a beam under distributed loading, deriving expressions for the moment about points A and B using cross products and integration.

Explore how a force on a solid both accelerates the center of mass and causes rotation; the moment quantifies this turning tendency, with torque equal to force times distance.

Describe a force couple as two parallel, opposite, equal forces that cause rotation without translation, via the resulting moment. Example: the forces exerted by your hand on a screwdriver.

Discover pure moments, a rotational force that causes rotation without translation, also known as a force couple or torque, applicable in 2d and 3d beam contexts with magnitude and direction.

Explore how constraint and reaction forces act at joints and contacts in machines and structures, use equilibrium to deduce unknown magnitudes and directions of forces and moments.

Draw free body diagrams with constraint forces by isolating the system, replacing joints with forces, and labeling components with double subscripts in 2d problems.