# Torque

Definition: Torque

Torque is the ability of a force to cause a body to rotate about a particular 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 caused by F about the axis through O is:

= Fl

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

l = lsin

where is the angle between the line of force and the line OB .

Note:

• We can also write torque as

 = Fl = Flsin = Fl (1)

where F = Fsin is the component of F perpendicular to OB .
• The units of torque are N 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:

 = + +... (2)

where = F1l1sin , etc. Be sure to get the signs right for each individual torque.

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