# Does the sum of the external torques on the rigid object have to equal zero in static equilibrium?

Oct 4, 2015

Yes, for an object in static equilibrium , the sum of the (external) forces acting on the object must be zero and the sum of the (external) torques acting on the object must be zero.

#### Explanation:

By definition, for an object to be in static equilibrium, the sum of the (external) forces acting on the object must be zero and the sum of the (external) torques acting on the object must be zero ($\sum F = 0$ and $\sum \tau = 0$).

Otherwise, the object would undergo liner acceleration (in the case of non-zero net forces) or angular acceleration (in the case of non-zero net torques).

In addition, most textbooks distinguish between

• static equilibrium, where

$\sum F = 0$ and $\sum \tau = 0$

and velocity and angular velocity are zero ($v = 0$ and $\omega = 0$)

• dynamic equilibrium, where

$\sum F = 0$ and $\sum \tau = 0$

but the linear and/or angular velocities are non-zero.