Statics/Equations of Statics

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Condition Of Equilibrium[edit]

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[edit]

F = ma

Trigonometry[edit]

Sine Law[edit]

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

Cosine Law[edit]

 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[edit]

Dot Product[edit]

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

Cross Product[edit]


  \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}