6.7. Static Equilibrium

A body is in static or dynamic equilibrium if the sum of all external forces acting on the body is zero.

\[ \sum \vec{F} = 0 \]

\[ \vec{F} = m\vec{a} \]

\[ \vec{a} = 0 \]

As force is a vector, we can write the equation for the sum of forces in component form:

\[ \sum \vec{F} = 0 \]

\[ \sum \vec{F} = \sum F_x \ \hat{i} + \sum F_y \ \hat{j} + \sum F_z \ \hat{k} \]

Which can be separated into 3 scalar equations of equalibrium:

\[ \sum F_x = 0 \]

\[ \sum F_y = 0 \]

\[ \sum F_z = 0 \]