Engineering Mechanics: Fundamentals and Equilibrium

Vocabulary practice flashcards covering fundamental mechanics concepts, systems of forces, vector algebra, equilibrium conditions, and support types.

Engineering Mechanics

The branch of Applied Science that deals with the laws and principles of Mechanics, along with their applications to engineering problems.

Mechanics

The branch of physics that deals with the motion of bodies under the influence of forces.

Statics

The sub-division of mechanics that deals with the study of bodies at rest.

Dynamics

The sub-division of mechanics that deals with the study of bodies in motion.

Kinematics

The branch of dynamics that deals with the study of motion without considering the forces causing it.

Kinetics

The branch of dynamics that deals with the study of motion considering both the forces and the mass of the body.

Primary Dimensions (Fundamental Quantities)

Basic measurable physical quantities that cannot be expressed in terms of others, specifically: Mass ($\text{M}$), Length ($\text{L}$), Time ($\text{T}$), Temperature ($\theta$), Electric Current ($\text{I}$), Luminous Intensity ($\text{J}$), and Amount of Substance ($\text{N}$).

Secondary Dimensions (Derived Quantities)

Physical quantities expressed in terms of primary dimensions, such as velocity ($[\text{L}\,\text{T}^{-1}]$), acceleration ($[\text{L}\,\text{T}^{-2}]$), force ($[\text{M}\,\text{L}\,\text{T}^{-2}]$), and pressure ($[\text{M}\,\text{L}^{-1}\,\text{T}^{-2}]$).

Law of Dimensional Homogeneity

A principle stating that every term in a physical equation must have identical dimensions, used to verify equations and derive relationships.

Rigid Body

An idealization in mechanics where an object does not deform under an applied load.

Particle

An idealization where an object is considered as a point mass when its physical size is negligible compared to the path of its motion.

Continuum

An idealization assuming matter is continuous and uniformly distributed, ignoring its atomic structure.

Law of Inertia (Newton's First Law)

The law stating that a body remains at rest or in uniform motion in a straight line unless acted upon by an external force.

Law of Acceleration (Newton's Second Law)

The law stating that force is directly proportional to the rate of change of momentum, represented by the equation $F = ma$.

Law of Action and Reaction (Newton's Third Law)

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

Parallelogram Law of Forces

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

Scalar

A physical quantity that has magnitude only, such as mass, time, energy, and temperature.

Vector

A physical quantity that possesses both magnitude and direction, such as force, velocity, displacement, and acceleration.

Collinear Forces

Forces whose lines of action lie along the exact same straight line.

Concurrent Forces

Forces whose lines of action intersect or meet at one single point.

Coplanar Forces

Forces whose lines of action lie within the same plane.

Coplanar Concurrent Forces

Forces that meet at a single point and whose lines of action also lie in the same plane.

Coplanar Non-Concurrent Forces

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

Non-Coplanar Concurrent Forces

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

Non-Coplanar Non-Concurrent Forces

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

Dot Product (Scalar Product)

An algebraic vector operation defined as $\mathbf{A} \cdot \mathbf{B} = AB\cos(\theta)$, yielding a scalar quantity such as Work ($W = \mathbf{F} \cdot \mathbf{d}$).

Cross Product (Vector Product)

An algebraic vector operation defined as $\mathbf{A} \times \mathbf{B} = AB\sin(\theta)\,\hat{\mathbf{n}}$, producing a vector perpendicular to the plane of $\mathbf{A}$ and $\mathbf{B}$ (applied in torque and moments).

Resultant Force Angle Formula

The formula used to determine the angle $\alpha$ that the resultant force makes with force $F_1$: $\tan(\alpha) = \frac{F_2 \sin(\theta)}{F_1 + F_2 \cos(\theta)}$.

Method of Resolution

A technique to find the resultant force by finding the algebraic sums of horizontal components ($\Sigma H$) and vertical components ($\Sigma V$), where $R = \sqrt{(\Sigma H)^2 + (\Sigma V)^2}$ and $\tan(\theta) = \frac{\Sigma V}{\Sigma H}$.

Cartesian Vector

A vector expressed in rectangular coordinate components as $\mathbf{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$, with magnitude $|\mathbf{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2}$.

Unit Vector

A vector having a magnitude of unity that points in the direction of vector $\mathbf{A}$, given by $\hat{a} = \frac{\mathbf{A}}{|\mathbf{A}|}$.

Position Vector

A vector that locates a point in space with respect to the origin, defined as $\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}$.

Displacement Vector

The difference between the final and initial position vectors of a particle, defined by $\mathbf{d} = \mathbf{r}_2 - \mathbf{r}_1$.

Moment of a Force About a Point

A measure of the rotational effect of a force about point $O$, defined mathematically as $\mathbf{M}_O = \mathbf{r} \times \mathbf{F}$, where $\mathbf{r}$ is the position vector from $O$ to the point of force application.

Moment of a Force About an Axis

The projection of the moment of a force onto a specific axis, computed as $M_{axis} = \mathbf{M}_O \cdot \hat{n}$, where $\hat{n}$ is the unit vector along that axis.

Couple

A system formed by two equal and opposite parallel forces separated by a perpendicular distance.

Couple Moment

The moment generated by a couple, given by $\mathbf{M} = \mathbf{r} \times \mathbf{F}$, which is a free vector independent of the choice of reference point.

Equivalent Force-Couple System

A system where an external force not acting through point $O$ is replaced by an identical concurrent force at $O$ plus a couple moment equal to $\mathbf{r} \times \mathbf{F}$.

Varignon's Theorem

The theorem stating that the moment of a resultant force about any point equals the sum of moments of its constituent component forces about the same point: $\mathbf{M}_O = \sum(\mathbf{r} \times \mathbf{F})$.

Distributed Load

A continuous load acting over a surface or length, equivalent to a single resultant force equal to the area under the distribution diagram acting directly at its centroid.

Particle Equilibrium Condition

The condition where the vector sum of all external forces acting on a particle equals zero ($\Sigma \mathbf{F} = 0$), satisfied when $\Sigma F_x = 0$, $\Sigma F_y = 0$, and $\Sigma F_z = 0$.

Free-Body Diagram (FBD)

A simplified sketch of an isolated body or particle showing all external applied forces, moments, support reactions, and necessary dimensions.

Lami's Theorem

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

Rigid Body Equilibrium

The mechanical state requiring both the sum of forces to equal zero (no translation, $\Sigma \mathbf{F} = 0$) and the sum of moments to equal zero (no rotation, $\Sigma \mathbf{M} = 0$).

Fixed Support

A support constraint that prevents both translation and rotation, providing three support reactions in 2D (two reaction forces and one reaction moment).

Pinned/Hinged Support

A support constraint that prevents translation in all directions while allowing rotation, providing two reaction force components (horizontal and vertical).

Roller Support

A support constraint that allows movement along the contact surface while preventing motion perpendicular to it, providing a single normal reaction force.

Beam

A structural member designed to carry transverse and axial loads, typically supported at its ends.

Simple Beam

A structural beam supported at two points by a hinge at one end and a roller at the other end.

Compound Beam

A structural configuration formed by connecting two or more beams together.