Torque

Definition: Torque

Torque is the ability of a force to cause a body to rotate about a particular axis.

  

Figure 8.1: Torque about an axis

In Figure 8.1, a force, F acts on an object at the point B . The object is pivoted so that it rotates about the point, O . The magnitude of the torque $\tau$ caused by F about the axis through O is:

$$\tau$$ = Fl_$\perp$

where l_$\perp$ (known as the moment arm of the force) is the perpendicular distance from the line of force to the axis through O :

l_$\perp$ = lsin $$\theta$$

where $\theta$ is the angle between the line of force and the line OB .

Note:

• We can also write torque as

  $$\tau \perp \theta \perp$$ (1)

  where F_$\perp$ = Fsin $\theta$ is the component of F perpendicular to OB .
• The units of torque are N $\cdot$ m.
• Torque is defined to be positive if it tends to rotate the object counterclockwise, and negative if it tends to rotate the object clockwise.
• If an object is acted on by more than one force the total torque is the sum of the torques due to the individual forces:

  $$\tau_{{\:\rm total}}^{} \tau_{1}^{} \tau_{2}^{}$$ (2)

  where $\tau_{1}^{}$ = F₁l₁sin $\theta_{1}^{}$ , etc. Be sure to get the signs right for each individual torque.