Biomedical Engineering Reference
In-Depth Information
line of action of force F
lever arm d
axis of rotation
F
direction of rotation
Fig. 2.1 A force F is applied at the center of an object. The line of action of the force F , the lever
arm d of the force F , and the axis of rotation through O are represented. The arrow indicates the
direction of rotation
M F ¼
Fd :
(2.1)
Its unit in the International System of Units (SI) is N m.
Figure 2.1 shows a force F applied at the center of an object. The rotation axis is
an imaginary line, perpendicular to the pivot point O, or fulcrum, of the object. The
lever arm d is perpendicular to the line of action of the force F , which tends to rotate
the object about the pivot point O clockwise; the magnitude of torque is M F ¼
Fd .
Now, if the force F with the same magnitude is applied in the opposite direction at
the same place, the direction of rotation changes; that is, the body will rotate
counterclockwise and the torque is given by M F ¼
Fd . Note that the axis of rotation
is always subjected to the reaction (not shown) to the force F . However, this reaction
force does not produce torque because its lever arm is equal to zero. You can imagine
that Fig. 2.1 represents a top view of a cross section of a door and the axis of rotation
is the hinge line and the force is applied to open the door.
If a force F of the same magnitude is now applied at the opposite extremity to the
axis, as can be seen in Fig. 2.2 , its torque will be twice that of Fig. 2.1 because the
lever arm will be 2 d , i.e., M F ¼
F (2 d ). In other words, it will now be twice as
easy to rotate a bar about its axis of rotation. That is what we usually do instinc-
tively to open a door or when we use a wrench to loosen a nut.
If we now apply a force F at the same place and with the same magnitude as that
of Fig. 2.2 , but with a different direction, as shown in Fig. 2.3 , we see that the torque
will be zero because the line of action of force will pass through the axis of rotation
and, in this case, the lever arm will be null. If we apply a force to a door in such a
way, we will never be able to either open or close it.
If we now apply a force F of the same intensity as that of Fig. 2.2 , but with a
different direction, as shown in Fig. 2.4 , we see that the torque, i.e., the turning
effect, is decreased, due to the fact that the lever arm which must be perpendicular
 
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