Answer to Essential Question 10.4: Quite a number of tools and gadgets exploit torque, in the
sense that they enable you to apply a small force at a relatively large distance from an axis, and
the tool converts that into a large force acting at a relatively small distance from an axis.
Examples include scissors, bottle openers, can openers, nutcrackers, screwdrivers, crowbars,
wrenches, wheelbarrows, and bicycles.
10-5 Three Equivalent Methods of Finding Torque
EXPLORATION 10.5 – Three ways to find torque
A rod of length L is attached to a wall by a
hinge. The rod is held in a horizontal position by a
string that is tied to the wall and attached to the end of
the rod, as shown in Figure 10.12.
Step 1 – In what direction is the torque applied by the
string to the rod, about an axis that passes through
the hinge and is perpendicular to the page? As we did
in previous chapters, it’s a good idea to draw a free-
body diagram of the rod (or at least part of a free-body
diagram, as in Figure 10.13) to help visualize what is
happening. For now the only force we’ll include on the free-
body diagram is the force of tension applied by the string
(we’ll go on to look at all the forces applied to the rod in
Exploration 10.8). Try placing your pen over the picture of
the rod. Hold the pen where the hinge is and push on the pen,
at the point where the string is tied to the rod, in the
direction of the force of tension. You should see the
pen rotate counterclockwise. Thus, we can say that the
torque applied by the string, about the axis through the
hinge, is in a counterclockwise direction.
Note that we are dealing with direction for torque much as we did for angular velocity.
The true direction of the torque can be found by curling your fingers on your right hand
counterclockwise and placing your hand, little finger down, on the page. When you stick out your
thumb it points up, out of the page. This is the true direction of the torque, but for simplicity we
can state directions as either clockwise or, as in this case, counterclockwise.
Now we know the direction of the torque, relative to an axis through the hinge, applied
by the string, let’s focus on determining its magnitude.
Step 2 – Measuring the distance r in Equation 10.9 along the bar, apply Equation 10.9 to find
the magnitude of the torque applied by the string on the rod, with respect to the axis passing
through the hinge perpendicular to the page.
Finding the magnitude of the torque means identifying the three variables, r, F, and !, in
Equation 10.9. In this case we can see from Figure 10.13 that the distance r is the length of the
rod, L; the force is the force of tension, ; and the angle ! is the angle between the line of
the force (i.e., the string) and the line the distance r is measured along (the rod), so ! is the angle
in Figure 10.13. In this case, then, applying Equation 10.9 tells us that the magnitude of the
torque is .
Chapter 10 – Rotation I Page 10 - 10
Figure 10.12: A rod attached to a wall at one
end by a hinge, and held horizontal by a string.
Figure 10.13: A partial free-body diagram for
the rod, showing the force of tension applied to
the rod by the string.
