Equilibrium problems  Equilibrium
Equilibrium problems
Lessons
Notes:
In this lesson, we will learn:
 Solving statics problems using both translational and rotational equilibrium
Notes:
 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)
Torque
$\tau = F_{\perp}d$
$\tau$: 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)
Conditions for Rotational Equilibrium
$\Sigma \tau = 0$ 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)

1.
Cable and beam in static equilibrium