Rotational Equilibrium

When we discussed static equilibrium in the chapter on forces and motion, we mentioned that there were additional constraints that were necessary for static equilibrium beyond the translational equilibrium condition discussed then. Now that we have introduced the concept of torque, we can come back to this issue.

For translational equilibrium we have seen that it is necessary that the sum of all forces vanishes,

$\sum$_i=1,...,n

_i = 0.

You can also, and perhaps more usefully, write this equation for the x- and y- components of the forces:

$\sum$_i=1,...,nF_x,i = 0

and

$\sum$_i=1,...,nF_y,i = 0.

It will not surprise you now that the condition for rotational equilibrium is

$\sum$_i=1,...,n

_i = 0

This condition can be rewritten in terms of clockwise torque $\tau$_cw and counterclockwise torque $\tau$_ccw

$\sum\tau$_cw -$\sum\tau$_ccw = 0.

An object is in mechanical static equilibrium if it is moving with constant linear velocity and angular velocity. Two special cases occur:

v = 0, translational static equilibrium
$\omega$ = 0, rotational static equilibrium