Mechanics I - Statics Vocabulary

Vocabulary flashcards covering key terms, fundamental concepts, Newton's laws, vector classifications, and force systems from Mechanics I - Statics.

Statics

The branch of mechanics that deals with the state of rest or motion of bodies moving with constant velocities.

Dynamics

The branch of mechanics in which bodies are subjected to acceleration.

Resistance of Materials

The branch of mechanics (Mechanics II) dealing with the relationships between external loads, the intensity of internal forces, and deformation response.

Space

A fundamental concept associated with the notion of the position of a point $P$ given in terms of three coordinates measured from a reference point or origin.

Time

A fundamental concept required to specify an event in terms of when and where it occurred.

Mass

A quantity used to characterize and compare bodies based on their response to Earth's gravitational attraction and resistance to changes in translational motion.

Force

A vector quantity representing the action of one body on another, characterized by its point of application, magnitude, and direction.

Newton's First Law

The principle stating that if the resultant force on a particle is zero, the particle will remain at rest or continue to move in a straight line.

Newton's Second Law

The principle stating that a particle subjected to a non-zero resultant applied force will experience an acceleration proportional to the force, expressed as $F = ma$.

Newton's Third Law

The principle stating that forces of action and reaction between two particles have equal magnitude, opposite sense, and the same line of action ($\vec{F}_{12} = -\vec{F}_{21}$).

Newton's Law of Gravitation

The law stating that two particles attract each other with equal and opposite forces calculated by $F = \hat{G} \frac{Mm}{r^2}$.

Universal Constant of Gravitation

The physical constant denoted by $\hat{G}$, equal to $66.73 \times 10^{-12}\,\text{m}^3/\text{kg}\cdot\text{s}^2$.

Fixed Vector (Bound Vector)

A vector possessing a well-defined point of application that cannot be changed without altering the results of an analysis.

Free Vector

A vector that may be moved freely in space without altering its effect on an analysis.

Sliding Vector

A vector that can be applied anywhere along its line of action without changing its effect on an analysis.

Equal Vectors

Vectors that share both the same magnitude and the same direction.

Negative Vector

A vector having the exact same magnitude as a given vector but pointing in the opposite direction.

Central Force System

A system of forces in which all lines of action intersect at a single point.

Static Equilibrium

The condition of a mechanical system where the resultant of all acting forces is equal to zero ($\vec{R} = \sum \vec{F}_i = 0$).

Method of Culmann

A method used to solve equilibrium problems for bodies subjected to four forces by combining pairs of forces into resultants $R_{12}$ and $R_{34}$.

Parallelogram Law

A principle of vector addition stating that two concurrent vectors can be replaced by a resultant represented by the diagonal of a parallelogram formed using those vectors.

Triangle Rule

A method of vector addition where the tail of the second vector is connected to the head of the first, forming a triangle with the resultant vector.

Polygon Rule

A graphical method for adding three or more vectors head-to-tail sequentially to determine their single resultant vector.

Law of Cosines and Law of Sines

Trigonometric laws used in vector triangles: Law of Cosines $C = \sqrt{A^2 + B^2 - 2AB \cos(c)}$ and Law of Sines $\frac{A}{\sin(a)} = \frac{B}{\sin(b)} = \frac{C}{\sin(c)}$.