Engineering Mechanics EN122 Comprehensive Learning Workbook (Lecture Notes)

A set of vocabulary flashcards covering key terms from the Engineering Mechanics lecture notes.

Free body diagram (FBD)

A diagram that isolates a body from its surroundings and shows all external forces acting on it, used to analyze equilibrium or motion.

Static equilibrium

A state in which the net external force and the net moment on a body are zero, so the body remains at rest or moves with constant velocity.

Lami's theorem

For three coplanar concurrent forces in equilibrium, each force is proportional to the sine of the angle opposite it: F1/sinα = F2/sinβ = F3/sinγ.

Varignon's theorem

In a force polygon, the resultant force and its moment can be found from the polygon of forces; the diagonal represents the resultant of coplanar forces.

Parallel axis theorem

Relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the centroid: I = I_cm + A d^2 (area moment of inertia).

Perpendicular axis theorem

For a planar lamina, the moment of inertia about the axis perpendicular to the plane equals the sum of the moments about the two perpendicular axes in the plane: Iz = Ix + I_y.

Perfect truss

A truss where m = 2j − 3, using the minimum number of members and joints to maintain shape; statically determinate.

Imperfect truss

A truss with m < 2j − 3, which does not maintain its shape under external loading (deficient).

A truss with m > 2j − 3, which is statically indeterminate and has excessive rigidity.

Redundant truss

Two-force member

A truss member that carries only two forces along its length (tension or compression); aligns with the member axis.

Method of joints

Analytical method for trusses where forces are found by solving equilibrium at each joint, usually with a maximum of two unknowns per joint.

Method of sections

A method to analyze trusses by cutting through the structure to expose up to three unknowns, solved using ΣX, ΣY, and ΣM.

Truss

A framework of straight members connected at joints, primarily carrying loads at joints; can be plane (2D) or space (3D).

Shear Force Diagram (SFD)

A plot showing how shear force varies along the length of a beam under loading.

Bending Moment Diagram (BMD)

A plot showing how the internal bending moment varies along the length of a beam under loading.

Centroid

The geometric center of an area, line, or volume; the point where the resultant of distributed loads can be considered to act.

Centre of gravity

The point where the total weight of a body can be considered to act; coincides with the centroid for uniform gravity.

Moment of inertia (I, area moment of inertia)

A measure of an area’s resistance to bending about a given axis; depends on shape and axis.

Mass moment of inertia

A measure of an object’s resistance to rotational motion about an axis, analogous to mass for linear motion.

Radius of gyration

k, where I = m k^2; describes how mass is distributed relative to an axis.

Free vector

A vector not fixed to a particular location; its magnitude and direction are independent of position.

SI base units

Fundamental units: metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), candela (luminous intensity).

Derived units (examples)

Units derived from base units, e.g., newton (N) for force, joule (J) for energy, watt (W) for power, pascal (Pa) for pressure, hertz (Hz) for frequency.

Newton's laws in context

Foundational relations used in kinetics and dynamics; motion is governed by forces and their accelerations (often treated via F = ma).

D'Alembert's principle

A method to convert dynamics problems into static-like form by introducing inertial forces, enabling equilibrium analysis.

Coefficient of friction (μ)

A scalar that characterizes the friction between two surfaces; μs for static and μk for kinetic friction.

Static friction

Frictional force that opposes initial relative motion up to a maximum μs N, before sliding begins.

Kinetic friction

Frictional force acting during sliding, equal to μk N, opposing motion along the contact surface.

Angle of repose

The steepest angle of descent relative to the horizontal to which an object on a slope will resist sliding; related to μ (tan of angle).

Transmissibility (principle of transmissibility)

The force’s line of action can be moved along the line of action without changing its external effect on a rigid body, under equilibrium.

Cantilever beam

A beam fixed at one end and free at the other, used to study deflection and bending moments.

Uniformly distributed load (UDL)

A load distributed evenly along a beam or element; often designated in beam problems.

Plane truss vs space truss

Plane (2D) truss lies in a single plane; space (3D) truss has members in multiple planes.

Three equations of equilibrium

ΣX = 0, ΣY = 0, and ΣM = 0 used to solve static problems for forces and moments.

Fundamental units vs derived units

Fundamental units are base quantities; derived units are combinations of base units (e.g., N, J, Pa).