whereris the distance from the axis to the point of application of
the force, andF⊥is the component of the force that is perpendicular
to the line joining the axis to the point of application.
The equation is stated with absolute value signs because the
positive and negative signs of force and torque indicate different
things, so there is no useful relationship between them. The sign
of the torque must be found by physical inspection of the case at
hand.
From the equation, we see that the units of torque can be writ-
ten as newtons multiplied by meters. Metric torque wrenches are
calibrated in N·m, but American ones use foot-pounds, which is also
a unit of distance multiplied by a unit of force. We know from our
study of mechanical work that newtons multiplied by meters equal
joules, but torque is a completely different quantity from work, and
nobody writes torques with units of joules, even though it would be
technically correct.p/Self-check.self-check A
Compare the magnitudes and signs of the four torques shown in figure
p. .Answer, p. 1056
How torque depends on the direction of the force example 6
.How can the torque applied to the wrench in the figure be ex-
pressed in terms ofr,|F|, and the angleθ?
.The force vector and itsF⊥component form the hypotenuse
and one leg of a right triangle,and the interior angle opposite toF⊥equalsθ. The absolute value
ofF⊥can thus be expressed asF⊥=|F|sinθ,leading to
|τ|=r|F|sinθ.262 Chapter 4 Conservation of Angular Momentum