Statics/Equations of Statics

Condition Of Equilibrium

When forces are in equilibrium, that is, there is no net force and the summation of the particle's moment, taken at any point, is equal to 0.

$\sum F_x = 0$

$\sum F_y = 0$

$\sum F_z = 0$

$\sum M_o = 0$

Newton's Second Law of Motion

F = ma

Trigonometry

Sine Law

${a \over sin A} = {b \over sin B} = {c \over sin C}$

Cosine Law

$a^2 = b^2 + c^2 - 2bc \cos A \$

$b^2 = a^2 + c^2 - 2ac \cos B \$

$c^2 = a^2 + b^2 - 2ab \cos C \$

Vector Relations

Dot Product

$\vec a \bullet \vec b = ab \cos \theta$

Cross Product

$\vec{a}\times\vec{b} = \begin{pmatrix}a_1 \\ a_2 \\ a_3\end{pmatrix} \times \begin{pmatrix}b_1 \\ b_2 \\ b_3 \end{pmatrix} = \begin{pmatrix} a_2b_3 - a_3b_2 \\ a_3b_1 - a_1b_3 \\ a_1b_2 - a_2b_1 \end{pmatrix} = \left|\vec{a}\right| \left|\vec{b}\right| \sin(\theta) \cdot \vec{e}$