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

${a \over sinA}={b \over sinB}={c \over sinC}$

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

${\vec {a}}\times {\vec {b}}={\begin{pmatrix}a_{1}\\a_{2}\\a_{3}\end{pmatrix}}\times {\begin{pmatrix}b_{1}\\b_{2}\\b_{3}\end{pmatrix}}={\begin{pmatrix}a_{2}b_{3}-a_{3}b_{2}\\a_{3}b_{1}-a_{1}b_{3}\\a_{1}b_{2}-a_{2}b_{1}\end{pmatrix}}=\left|{\vec {a}}\right|\left|{\vec {b}}\right|\sin(\theta )\cdot {\vec {e}}$