Engineering Mechanics – Module 1: Statics of Particles

Vocabulary flashcards covering key terms and principles from Engineering Mechanics (Module 1: Statics of Particles).

Mechanics

The science that describes and predicts the conditions of rest or motion of bodies under the action of forces.

Engineering Mechanics

Application of mechanics principles to solve engineering problems involving forces and motion.

Statics

Branch of mechanics that deals with bodies at rest or in equilibrium under the action of forces.

Dynamics

Branch of mechanics that studies bodies in motion under the influence of forces.

Kinematics

Study of motion without regard to the forces that cause it (displacement, velocity, acceleration).

Kinetics

Study of motion that considers the forces causing the motion.

Rigid Body

An idealized solid body in which deformation is neglected; the distance between any two points remains constant.

Particle

A body whose dimensions are negligible compared with the distances involved in the problem.

Force

Vector quantity representing the action of one body on another, characterized by magnitude, direction, and line of action.

Magnitude of a Force

Numerical value that expresses the strength or size of the force (e.g., 100 N).

Line of Action

Infinite straight line along which a force acts.

Concurrent Forces

Forces whose lines of action all intersect at a common point.

Coplanar Forces

Forces whose lines of action lie in the same plane.

Collinear Forces

Forces that have the same line of action.

Resultant Force

Single force that has the same external effect as a system of forces acting on a body.

Equilibrant

Force that is equal in magnitude but opposite in direction to the resultant; it brings the system into equilibrium.

Equilibrium of a Particle

Condition in which the vector sum of all forces acting on a particle is zero.

Free-Body Diagram (FBD)

Sketch of an isolated body showing all external forces and reactions acting on it.

Vector

Physical quantity having both magnitude and direction (e.g., force, velocity).

Scalar

Physical quantity described completely by magnitude alone (e.g., mass, temperature).

Unit Vector

Dimensionless vector of magnitude one that indicates direction along a coordinate axis or line.

Triangle Law of Addition

If two vectors are represented in sequence tip-to-tail, their resultant is the vector from the tail of the first to the tip of the second.

Parallelogram Law of Addition

Two vectors acting from the same point can be replaced by their diagonal (resultant) of the parallelogram constructed on them.

Polygon Law of Forces

Extension of triangle law: if several vectors are arranged tip-to-tail, the closing side represents the resultant.

Principle of Transmissibility

A force may be applied anywhere along its line of action without changing the external effect on a rigid body.

Varignon’s Theorem (Law of Moments)

Moment of a force about any point equals the algebraic sum of the moments of its components about the same point.

Lami’s Theorem

For three coplanar, concurrent forces in equilibrium, each force is proportional to the sine of the angle between the other two forces.

Newton’s First Law

A body remains at rest or moves with constant velocity unless acted upon by a resultant force.

Newton’s Second Law

Resultant force acting on a particle equals the product of its mass and acceleration (F = m a).

Newton’s Third Law

For every action, there is an equal and opposite reaction.

Newton’s Law of Gravitation

Attractive force between two masses is F = G M m / r², acting along the line joining them.

Dry Friction (Coulomb Friction)

Resistance to sliding that occurs between two dry surfaces in contact.

Coefficient of Friction (μ)

Ratio of limiting friction to the normal reaction between two surfaces.

Angle of Friction

Angle between the resultant reaction and the normal reaction when sliding impends; tan φ = μ.

Moment of a Force

Measure of the tendency of a force to rotate a body about a point or axis; equal to force magnitude times perpendicular distance.

Couple

Two equal, parallel, opposite forces whose lines of action are separated by a distance, producing pure rotation.

System of Forces

Group of two or more forces acting on a body.

Coplanar Non-concurrent Forces

Forces in the same plane whose lines of action do not meet at a single point.

Rectangular Components of a Force

Projection of a force onto mutually perpendicular axes, usually denoted Fx and Fy (and Fz in 3-D).

Direction Cosines

Cosines of the angles between a vector and the coordinate axes (cos θx, cos θy, cos θz).

Unit Conversion

Process of changing a quantity expressed in one set of units to an equivalent value in another set.

Moment of Inertia (Area)

Second moment of area measuring resistance of a cross-section to bending about an axis.

Radius of Gyration

Distance from an axis at which the entire area could be concentrated without changing the moment of inertia; k = √(I/A).

Centroid

Geometric center of an area, line, or volume; point where the first moments of area are zero.

Pappus–Guldinus Theorem

Relates the surface area or volume generated by revolving a plane curve or area about an axis to the path of its centroid.

Principle of Virtual Work

For a system in equilibrium, the total virtual work of all external forces during any virtual displacement is zero.

Beam

Structural member subjected mainly to transverse loads that induce bending moments and shear forces.

Truss

Structure composed of slender members joined together at their ends, usually forming triangular units and carrying loads at joints.

Method of Joints

Technique for determining internal forces in truss members by applying equilibrium to each joint.

Method of Sections

Technique to find forces in specific truss members by cutting through the truss and applying equilibrium to a section.

Instantaneous Center of Rotation

Point in a plane body undergoing general motion that has zero instantaneous velocity at a given instant.

Impulse–Momentum Principle

Change in momentum of a particle equals the impulse of the resultant force acting over a time interval.

Work–Energy Principle

Work done by all forces on a particle equals the change in its kinetic energy.