Summarizing the Second Condition For Equilibrium

Summary

• The second condition assures those torques are also balanced. Torque is the rotational equivalent of a force in producing a rotation and is defined to be

  \(\tau =\text{rF}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \)

  where \(\tau \) is torque, \(r\) is the distance from the pivot point to the point where the force is applied, \(F\) is the magnitude of the force, and \(\theta \) is the angle between \(\mathbf{\text{F}}\) and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm \({r}_{\perp }\) is defined to be

  \({r}_{\perp }=r\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \)

  so that

  \(\tau ={r}_{\perp }F.\)

• The perpendicular lever arm \({r}_{\perp }\) is the shortest distance from the pivot point to the line along which \(F\) acts. The SI unit for torque is newton-meter \(\text{(N·m)}\). The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero:

  \(\text{net}\phantom{\rule{0.25em}{0ex}}\tau =0\)

  By convention, counterclockwise torques are positive, and clockwise torques are negative.

Glossary

torque

turning or twisting effectiveness of a force

perpendicular lever arm

the shortest distance from the pivot point to the line along which \(\mathbf{\text{F}}\) lies

SI units of torque

newton times meters, usually written as N·m

center of gravity

the point where the total weight of the body is assumed to be concentrated