MAE 2103 - Statics Vocabulary Review

Vocabulary flashcards covering core definitions, unit conversions, physical principles, and vector mathematics from MAE 2103 Statics introductory notes.

Mechanics

The study of forces, deformation, and motion.

Constitutive Laws

The branch of mechanics describing material behavior, specifically detailing how applied loads cause deformation.

Kinematics

The branch of mechanics concerned with the geometry of motion and distortion.

Kinetics

The branch of mechanics dealing with the laws that relate forces to motion.

Rigid Body Mechanics

The simplification of mechanics based on the assumption that materials do not undergo deformation.

Newton's First Law

The principle stating that when the sum of forces on a particle is zero ($\Sigma F = 0$), its velocity remains constant, and a stationary particle remains stationary.

Newton's Second Law

The law of linear motion defined by $\Sigma F = m a$, establishing the relationship between net force, mass, and acceleration, where $1\,\text{N} = 1\,\text{kg}\cdot\text{m/s}^2$.

Rotational Motion Law

The law of angular momentum given by $\Sigma M = I \alpha$, where a net turning effect $M$ causes angular acceleration $\alpha$ proportional to the moment of inertia $I$.

Action-Reaction Law

The principle stating that forces between two particles are equal in magnitude and opposite in direction, such that every action has an equal and opposite reaction.

Action

An external force or load applied to a physical system.

Reaction

The response force produced by a physical system in opposition to an applied action.

Statics

The branch of mechanics analyzing rigid bodies in equilibrium where acceleration and deformation are negligible, satisfying $\Sigma F = 0$ and $\Sigma M = 0$.

Dynamics

The branch of mechanics analyzing systems with non-negligible acceleration where mass matters and $\Sigma F = m a \neq 0$ or $\Sigma M = I \alpha \neq 0$.

Significant Figures

The number of accurate digits in a numerical value, counted left to right starting with the first nonzero digit.

Scalar Quantity

A physical quantity completely described by a single real number representing magnitude, such as mass, time, temperature, or energy.

Vector Quantity

A physical quantity requiring both a magnitude and a direction to be completely defined, such as position, velocity, or force.

Triangle Rule

A vector addition method where the tail of vector $V$ is placed at the head of vector $U$, and the sum $U + V$ is drawn from the tail of $U$ to the head of $V$.

Parallelogram Rule

A vector addition method where the tails of vectors $U$ and $V$ are placed together, and their sum is represented by the diagonal of the resulting parallelogram.

Resultant Force

A single force $F_R$ that produces the same overall physical effect as multiple individual forces combined ($F_R = F_1 + F_2 + F_3 + \dots$).

Unit Vector

A dimensionless vector with a magnitude equal to $1$ that is used exclusively to specify a spatial direction ($e = \frac{U}{|U|}$).

Cartesian Unit Vectors in 2D

The perpendicular unit vectors $i$ (positive $x$-direction) and $j$ (positive $y$-direction), used to express a vector as $U = U_x i + U_y j$.

Position Vector

A vector $r_{AB}$ specifying spatial direction from point $A(x_A, y_A)$ to point $B(x_B, y_B)$, defined as $r_{AB} = (x_B - x_A)i + (y_B - y_A)j$.

Law of Cosines

A trigonometric rule applied to vector triangles defined by $c^2 = a^2 + b^2 - 2ab \cos(\gamma)$, useful when two sides and the included angle are known.

Law of Sines

A trigonometric ratio for vector triangles given by $\frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)}$.

Right-Handed Coordinate System

A three-dimensional coordinate system in which curling the fingers of the right hand from the positive $x$-axis to the positive $y$-axis causes the thumb to point along the positive $z$-axis.

Cartesian Unit Vectors in 3D

The set of mutually perpendicular unit vectors $i$, $j$, and $k$ aligned along the positive $x$, $y$, and $z$ axes, representing vectors in the form $U = U_x i + U_y j + U_z k$.

3D Vector Magnitude

The scalar length of a 3D vector calculated using the extended Pythagorean theorem as $|U| = \sqrt{U_x^2 + U_y^2 + U_z^2}$.