Engineering Mechanics

Force

An influence that can change the motion of an object; a push or pull.

Equilibrium

A state where the net force and net moment acting on a body are zero, resulting in no acceleration.

Free-Body Diagram (FBD)

A diagram showing a body isolated from its surroundings, with all external forces and moments acting on it represented by vectors.

Kinematics

The branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion.

Kinetics

The branch of mechanics that deals with the relationship between motion and its causes (forces and torques).

Momentum

The product of the mass and velocity of an object (p = mv).

Centroid of a Composite Area

Used in Statics for finding the resultant center of an area.

\bar{x} = \frac{\sum A_i x_i}{\sum A_i}, \bar{y} = \frac{\sum A_i y_i}{\sum A_i}

Moment of Inertia (Area)

Resistance of a cross-section to bending.

I = \int y² dA

Newton's Second Law of Motion

Fundamental law relating force, mass, and acceleration.

\sum \vec{F} = m \vec{a}

Work-Energy Theorem

Relates work done by net force to change in kinetic energy.

W_1-2 = T₂ - T₁ = \frac{1}{2}mv₂^2 - \frac{1}{2}mv₁^2

Impulse-Momentum Theorem

Relates impulse of net force to change in linear momentum.

\int_{t_1}^{t₂} \sum \vec{F} dt = m\vec{v}_2 - m\vec{v}_1

Conservation of Energy

Applies when only conservative forces do work.

T₁ + V₁ = T₂ + V₂

Conservation of Momentum

Applies when the net external impulse is zero.

\sum m_i \vec{v}_{i,1} = \sum m_i \vec{v}_{i,2}