Static equilibrium problems

In this lesson, we will learn:

• Solving statics problems using both translational and rotational equilibrium

• An object or group of objects that are not moving are in static equilibrium.
• In static equilibrium, the conditions for both translational and rotational equilibrium must be met.

$\Sigma F = 0 N$

or equivalently:

$\Sigma F_{x} = 0 N$ and $\Sigma F_{y} = 0 N$

$\Sigma F:$ sum of all forces, in newtons (N)

$\Sigma F_{x}:$ sum of all force components in x direction, in newtons (N)

$\Sigma F_{y}:$ sum of all force components in y direction, in newtons (N)

$\tau = F_{\perp}d$

$\tau$: torque, in newton meters (N·m)

$F_{\perp}:$ component of force perpendicular to $d$, in newtons (N)

$d:$ distance from point of rotation, in meters (m)

$\Sigma \tau = 0$ N·m

or simpler equation:

total $CW$ $\tau$ = total $CCW$ $\tau$

$\Sigma \tau :$ sum of all torques, in newton meters (N·m)

total $CW$ $\tau$: magnitude of all torques in the clockwise direction, in newton meters (N·m)

total $CCW$ $\tau$: magnitude of all torques in the counterclockwise direction, in newton meters (N·m)