A force may be thought of as a push or
pull in a specific direction. When a force is applied to an object,
in the direction of the force according to Newton's
laws of motion. The object may also experience a
rotation depending on how the object is confined
and where the force is applied. A hanging door is an excellent example of
this type of motion. When you push on a door it can not freely translate
because it is confined (or pinned) by the hinges. It does, however, rotate
on the hinges. The rotation itself depends on where you apply the force.
As you get closer to the hinge, you must apply a larger force to make the
door swing. As you get farther from the hinge, you can apply a smaller
force to make the door swing.
The product of the force and the perpendicular distance to a pivot (or hinge) is
called the torque or the moment. Torques produce rotations
in the same way that forces produce translations. Namely, an object at
rest, or rotating at a constant angular velocity continues to do so
until it is subject to an external torque. A torque produces an angular
acceleration or change in angular velocity. If an object is not pinned,
it rotates about its
center of gravity when acted upon by an external
force. The distance used in the calculation of the torque is then the
distance from the center of gravity perpendicular to the applied force.
A force (F) is a vector quantity, which means that it has both a magnitude and
a direction associated with it. The direction is important. A force directed due north
produces a different result on an object than a force of the same magnitude, but directed
to the east. The distance (L) used to determine the torque (T) is the distance from the
pivot (p) to the force, but measured perpendicular to the direction of the force. We show
three examples on the figure of this principle as applied to a weight (blue) which is
acting on an arm (red bar). In Example 1, the force (weight) is applied perpendicular
to the arm. In this case, the perpendicular distance is the actual length of the bar and the
torque is equal to the product of the length and the force.
T = F * L
In Example 2, the same force is applied to the arm, but the force now acts right through the
pivot. In this case, the distance from the pivot perpendicular to the force is zero
So, in this case, the torque is also zero. Think of the hinged door example; if you push on
the edge of the door, towards the hinge, the door doesn't move because the torque is zero.
Example 3 is the general case in which the force is applied at some angle a to
the arm. The perpendicular distance is given by
as the length of the arm (L)
times the cosine (cos) of the angle.
T = F * L * cos(a)
Examples 1 and 2 can be derived from this general formula, since the cosine of 0 degrees
is 1.0 (Example 1), and the cosine of 90 degrees is 0.0 (Example 2).
The Wright brothers used the torque generated by aerodynamic surfaces
to stabilize and control their aircraft.
On an airplane, each control surfaces produces
These forces are applied at some distance from the
cause the aircraft to rotate. The
elevators produce a
pitching moment, the
rudder produce a
yawing moment, and the
wing warping produced a
rolling moment. The ability to vary the amount of
the force and the moment allowed the pilot to maneuver
- Re-Living the Wright Way
- Beginner's Guide to Aeronautics
- NASA Home Page