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} $$