Engineering Mechanics: Statics, Dynamics, and Structural Principles

Vocabulary practice flashcards covering fundamental concepts, definitions, physical principles, and analytical theorems from engineering mechanics.

Mechanics

The oldest branch of physical sciences that deals with energy and forces and their effect on bodies, predicting or determining the conditions of rest or motion under the action of forces.

Rigid Body Mechanics

The study of the motion and behavior of idealized solid objects that do not deform under force.

Statics

A branch of mechanics dealing with bodies at rest or in equilibrium, where all forces and moments are balanced out.

Dynamics

A branch of mechanics dealing with rigid bodies in motion, focusing on how forces and moments cause motion or change the state of a body.

Kinematics

A subdivision of dynamics that deals with the motion of objects without considering the forces causing that motion.

Kinetics

A subdivision of dynamics that deals with the motion of objects and the forces that cause or affect those motions.

Deformed Body Mechanics

The study of how solid materials change shape and deform under applied forces.

Fluid Body Mechanics

The study of fluid (liquids and gases) behavior at rest and in motion, subdivided into fluid statics (hydrostatics) and fluid dynamics (hydrodynamics).

Particle

An idealization treating an object as a dimensionless point whose mass is concentrated at its center of mass, ignoring size and shape to simplify analysis.

Rigid Body

An idealized solid object assumed not to change shape or deform under stress or force, regardless of the magnitude of force applied.

Point Load

A concentrated force applied at a single point, used to simplify the analysis of distributed forces acting on a body or structure.

Mass

A measure of the amount of material in an object directly related to the number and types of atoms present, representing the inertia of a body against changes in velocity, measured in $kg$ in the SI system.

Scalar Quantity

A physical quantity that possesses only magnitude, such as time, volume, density, speed, energy, and mass.

Vector Quantity

A physical quantity possessing both magnitude and direction that must obey the parallelogram and triangle laws of addition, such as displacement, velocity, acceleration, force, and moment.

Unit Vector

A vector with a magnitude of $1$ used to indicate direction, typically denoted as $\hat{n}$ or $\hat{i}, \hat{j}, \hat{k}$ for cartesian axes.

Orthogonal Vectors

Vectors that are perpendicular to each other, having a dot product equal to zero.

Force

An action exerted by one body upon another that changes or tends to change the state of motion of the body, characterized by its magnitude, point of application, line of action, and sense.

Line of Action of a Force

The straight line passing through the point of application along which a force tends to move a body.

Unit Newton Force

The force which, when acting on a body of mass $1\,kg$, produces an acceleration of $1\,m/s^2$.

Reactions

The force exerted by a support or resting surface in response to external loads or actions applied to a body.

Free Body Diagram (FBD)

A simplified drawing showing only the object of interest with all supporting surfaces removed and replaced by the corresponding reaction forces and applied loads.

Moment of a Force

A vector quantity defined about a point as the product of the force magnitude and the perpendicular distance from that point to the line of action of the force ($M = F \times d$).

Couple

A system formed by two equal, unlike, parallel, non-collinear forces that produces purely rotary motion without linear motion, having a resultant of zero.

Lever Arm of a Couple

The perpendicular distance separating the two parallel forces that constitute a couple.

Equilibrium

The state of a body where the resultant of all external forces acting upon it is zero, keeping the body at rest or in uniform motion.

Conditions of Equilibrium for Coplanar Non-Concurrent Forces

The three analytical requirements for a coplanar non-concurrent force system to remain in equilibrium: $\Sigma F_x = 0$, $\Sigma F_y = 0$, and $\Sigma M = 0$.

Newton's First Law of Motion

The law stating that every body continues in its state of rest or uniform motion in a straight line unless acted upon by some external unbalanced force.

Newton's Second Law of Motion

The law stating that the rate of change of momentum of a body is directly proportional to the unbalanced force acting on it and occurs in the direction of that force ($F = m a$).

Newton's Third Law of Motion

The law stating that to every action there is always an equal and opposite reaction.

Newton's Law of Gravitational Attraction

The principle stating that two bodies exert mutual forces of attraction along the line connecting their centers of mass, expressed by $F = \frac{G m_1 m_2}{r^2}$, where $G = 6.67 \times 10^{-11}\,Nm^2/kg^2$.

Collinear Force System

A system of forces whose lines of action all lie along the exact same straight line.

Concurrent Force System

A force system where the lines of action of all applied forces pass through a single common point.

Resolution of a Force

The process of replacing a single force by two or more component forces that produce the same physical effect as the original force.

Composition of Forces

The process of combining two or more forces into a single equivalent force called the resultant force.

Resultant Force

A single force that can replace a system of forces and produce the exact same mechanical effect on a body.

Parallelogram Law of Forces

A principle stating that if two concurrent forces are represented in magnitude and direction by the adjacent sides of a parallelogram, their resultant is represented by the diagonal passing through their common point.

Principle of Transmissibility

The principle stating that the point of application of an external force on a rigid body can be moved to any other point along its line of action without altering the external effects or reactions on the body.

Varignon's Theorem

The theorem stating that the moment of a force about any point is equal to the algebraic sum of the moments of its components about the same point, or that the sum of moments of a coplanar force system equals the moment of their resultant.

Lami's Theorem

A theorem stating that if three coplanar forces acting at a single point are in equilibrium, each force magnitude is proportional to the sine of the angle between the other two forces: $\frac{F_1}{\sin(\alpha)} = \frac{F_2}{\sin(\beta)} = \frac{F_3}{\sin(\gamma)}$.

Centre of Gravity (CG)

An imaginary balancing point of a three-dimensional body possessing mass through which the resultant gravitational attraction force acts, and around which the body can balance in any orientation.

Centroid

A geometrical point corresponding to the center of gravity for massless geometrical figures such as lines, curves, and planar areas (two-dimensional objects).

Moment of Inertia of a Planar Section

Also known as the second moment of area, it is a geometric property measuring a section's resistance to flexural bending about a specified axis, given by $I_x = \int y^2\,dA$ or $I_y = \int x^2\,dA$.

Parallel Axis Theorem

A theorem stating that the moment of inertia of an area with respect to any axis equals the moment of inertia about its centroidal parallel axis plus the product of the area and the square of the distance between the two axes ($I = I_G + A h^2$).

Perpendicular Axis Theorem

A theorem stating that the polar moment of inertia of a plane lamina about an axis perpendicular to its plane ($I_{zz}$) equals the sum of its moments of inertia about two mutually perpendicular in-plane axes intersecting at that point ($I_{zz} = I_{xx} + I_{yy}$).

Radius of Gyration

The theoretical distance ($k$) from an axis at which the entire area of a lamina could be concentrated such that the moment of inertia remains unchanged, defined by $k = \sqrt{\frac{I}{A}}$.

Frictional Force

A passive, self-adjusting tangential force that automatically appears between contacting surfaces upon the application of a tractive force to oppose impending or relative sliding motion.

Limiting Friction

The maximum static frictional resistance ($F_{\text{max}}$) developed between surfaces at the threshold of impending motion, beyond which sliding commences.

Impending Motion

The critical equilibrium state of an object on the verge of slipping across a contact surface, occurring when static friction reaches its limiting value ($F_{\text{max}}$).

Coefficient of Friction

The dimensionless ratio of the limiting frictional force to the normal reaction force between two contacting surfaces ($\mu = \frac{F_{\text{max}}}{R_N}$).

Angle of Friction ($\phi$)

The angle between the resultant total contact reaction ($R_T$) and the normal reaction ($R_N$) at the condition of limiting friction, defined by $\tan(\phi) = \mu$.

Angle of Repose ($\alpha$)

The maximum inclination angle of an inclined plane at which a resting body remains in equilibrium solely under the action of gravity and friction, mathematically equal to the angle of friction ($\alpha = \phi$).

Cone of Friction

A right circular cone generated at the contact point between two bodies, having its vertex at the point of contact, its central axis along the normal reaction ($R_N$), and a semi-vertical angle equal to the angle of friction ($\phi$).

Belt Friction Formula

The exponential relation governing the tension ratio between the tight side ($T_2$) and the slack side ($T_1$) of a flexible band or rope wrapped over a cylindrical drum: $T_2 = T_1 e^{\mu \theta}$, where $\theta$ is the angle of wrap in radians.

Coefficient of Rolling Resistance

The horizontal distance ($b$) by which the ground reaction force shifts ahead of the wheel's center under loading to create a resisting moment ($W b$), measured in units of length ($mm$).

Perfect Truss

An idealized pin-jointed skeletal structure that contains the exact minimum number of members necessary to maintain geometric stability without collapsing, satisfying $n = 2j - 3$.

Deficient Truss

A truss structure that contains fewer members than the minimum required for geometric stability, satisfying $n < 2j - 3$.

Redundant Truss

A truss structure that contains more members than the minimum required for stability, satisfying $n > 2j - 3$.

Two Force Member

A structural member subjected to loads at only two pin points, requiring the two forces to be equal in magnitude, opposite in direction, and collinear along the axis joining the pins.

Zero Force Member

A truss member that carries zero internal axial force under a specific loading configuration, utilized primarily to provide structural stability during assembly or handle alternate load paths.

Mechanics

The oldest branch of the physical sciences that deals with energy and forces and their effect on bodies, describing or predicting the conditions of rest or motion of bodies under the action of forces.

Rigid Body Mechanics

The study of the motion and behavior of idealized solid objects that do not deform under force.

Statics

The branch of mechanics that deals with bodies at rest or in equilibrium, where forces and moments are balanced out and bodies remain stationary or move with constant velocity.

Dynamics

The branch of mechanics that deals with bodies in motion and how forces and moments cause motion or change the state of a body.

Kinematics

A subdivision of dynamics that deals with the motion of objects without considering the forces causing the motion.

Kinetics

A subdivision of dynamics that deals with the motion of objects and the forces that cause or affect that motion.

Deformed Body Mechanics

The study of how solid materials change shape and deform under applied forces.

Fluid Body Mechanics

The study of the behavior of fluids (liquids and gases) at rest (hydrostatics) and in motion (hydrodynamics).

Particle

An idealization of an object as a dimensionless point located at its center of mass, used when its size is negligible compared to the overall dimensions of the problem.

Rigid Body

An idealized body that will not deform or change its shape regardless of the magnitude of the force applied to it.

Point Load

A concentrated force applied at a single point, used to simplify the analysis of distributed forces acting on a structure.

Vector Quantity

A physical quantity that possesses both magnitude and direction, and obeys the parallelogram law of addition.

Dot Product

A mathematical operation that multiplies two vectors together to produce a scalar quantity.

Unit Vector

A vector having a magnitude of $1$, typically denoted as $\hat{n}$ or $\hat{i}, \hat{j}, \hat{k}$, used solely to indicate direction.

Collinear Vectors

Vectors that lie along the same straight line or can be represented as scalar multiples of each other.

Orthogonal Vectors

Vectors that are perpendicular to each other and have a dot product equal to zero.

Free Vector

A vector whose action is not confined to or associated with a unique line in space, and which can be moved parallel to itself without changing its effect.

Sliding Vector

A vector that has a unique line of action in space but not a unique point of application, as seen with external forces on a rigid body.

Bound Vector

A vector that has a fixed initial point of application and cannot be moved without altering its effect, such as a force acting on a deformable body.

Force

An action that changes, or tends to change, the state of motion of a body upon which it acts, or the action exerted by one body upon another.

Line of Action of Force

The straight line through the point of application along which a force tends to move the body to which it is applied.

Reaction

The force exerted by a support or boundary surface in response to external loads or actions applied to a body.

Roller Support

A type of support that restrains movement in the vertical direction while allowing rotation and horizontal translation.

Pin Support / Hinge Support

A type of support that restrains movement in both vertical and horizontal directions while allowing rotation.

Fixed Support

A type of support that prevents both translation and rotation in any direction.

Free Body Diagram (FBD)

A simplified diagram showing only the isolated body of interest with all physical supports removed and replaced by the corresponding reaction forces and applied loads.

Unit Newton Force

That force which, when acting on a body of mass $1\,\text{kg}$, produces an acceleration of $1\,\text{m/s}^2$ in it.

Moment of a Force

The product of the force magnitude and the perpendicular distance from a given point to the line of action of the force.

Couple

A system formed by two equal, unlike, parallel, non-collinear forces that produces purely rotary motion with a resultant force equal to zero.

Lever Arm of a Couple

The perpendicular distance separating the two parallel lines of action of the forces forming a couple.

Equilibrium

The state of a body wherein the resultant force and resultant moment acting on it are zero, keeping the body unaffected in its state of rest or constant motion.

Newton's First Law of Motion

The law stating that every body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external agency to change that state.

Newton's Second Law of Motion

The law stating that the rate of change of momentum of a body is directly proportional to the unbalanced force acting on it and occurs in the direction of that force.

Newton's Third Law of Motion

The law stating that to every action there is an equal and opposite reaction.

Newton's Law of Gravitational Attraction

The law stating that two bodies exert mutual attractive forces directed toward each other's center of mass, expressed by $F = \frac{G m_1 m_2}{r^2}$.

Coplanar Force System

A force system in which the lines of action of all forces lie within the same plane.

Concurrent Force System

A system of forces whose lines of action all intersect at a single common point.

Resolution of Forces

The process of breaking down or replacing a single force into two or more component forces that have the same combined effect as the original force.

Composition of Forces

The process of combining two or more forces to obtain a single resultant force that produces the identical external effect.

Resultant Force

A single force that can replace a system of forces and produce the exact same mechanical effect on a body as all the original forces combined.

Parallelogram Law of Forces

The principle stating that if two concurrent forces acting on a body are represented by adjacent sides of a parallelogram, their resultant is represented in magnitude and direction by the diagonal passing through their point of concurrency.