Last modified on 5 February 2008, at 23:22

Statics/Equations of Statics

Condition Of EquilibriumEdit

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 MotionEdit

F = ma

TrigonometryEdit

Sine LawEdit

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

Cosine LawEdit

 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 RelationsEdit

Dot ProductEdit

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

Cross ProductEdit


  \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}