A Classical Approach of Newtonian Mechanics

8 ROTATIONAL MOTION 8.7 Torque

O

Figure 80: Definition of the length of the level arm, l.

velocity, then torque must be analogous to force. In other words, torque is the

rotational equivalent of force.

It is clear, from Eq. (8.56), that a torque is the product of the magnitude of
the applied force, f, and some distance l = b sin θ. The physical interpretation

of l is illustrated in Fig. 80. If can be seen that l is the perpendicular distance of

the line of action of the force from the axis of rotation. We usually refer to this

distance as the length of the lever arm.

In summary, a torque measures the propensity of a given force to cause the

object upon which it acts to twist about a certain axis. The torque, τ, is simply

the product of the magnitude of the applied force, f, and the length of the lever

arm, l:
τ = f l. (8.57)

Of course, this definition makes a lot of sense. We all know that it is far easier

to turn a rusty bolt using a long, rather than a short, wrench. Assuming that we

exert the same force on the end of each wrench, the torque we apply to the bolt

is larger in the former case, since the perpendicular distance between the line of

action of the force and the bolt (i.e., the length of the wrench) is greater.

f

  (^) f l

b (^) P
l