# General Mechanics/Statics

If a rigid body is initially at rest, it will remain at rest if and
only if the sum of all the forces and the sum of all the torques
acting on the body are zero. As an example, a mass balance with arms
of differing length is shown in figure above.
The balance beam is subject to three forces pointing upward or downward, the
tension *T* in the string from which the beam is suspended and the
weights *M*_{1}g and *M*_{2}g exerted on the beam by the two suspended
masses. The parameter *g* is the local gravitational field and the
balance beam itself is assumed to have negligible mass. Taking upward
as positive, the force condition for static equilibrium is

Defining a counterclockwise torque to be positive, the torque balance computed about the pivot point in figure 10.7 is

where *d*_{1} and *d*_{2} are the lengths of the beam arms.
The first of the above equations shows that the tension in the
string
must be

while the second shows that

Thus, the tension in the string is just equal to the weight of the masses attached to the balance beam, while the ratio of the two masses equals the inverse ratio of the associated beam arm lengths.