Game Development Reference
In-Depth Information
Figure 12.19. On the left, the line of action passes through the center of mass, resulting in
linear acceleration but no torque. On the right, a couple produces a torque but
no linear acceleration.
If you blow on the door or whack it close to the hinge (shorter lever arm),
your action won't cause the door to rotate as easily if you do the same thing
nearer to side with the handle (longer lever arm). That's exactly why we
put door handles on the side opposite the hinge: to make it easier to open
the door!
The relationship between torque and force is an important one to under-
stand. Any force applied to a body can produce both a linear acceleration
and a torque. Of course, it is the net force and torque that determine the
acceleration(s) of the body. Two key examples in Figure 12.19 illustrate
this point. On the left, a force is acting along a line that passes through
the center of mass, resulting in no torque. In this case, sinĪ† = 0 since the
line of action of the force is parallel to the lever arm. The right side of Fig-
ure 12.19 shows a different extreme case: two forces with equal magnitudes
but opposite directions are acting on opposite lever arms. A pair of forces
coordinated like this are known as a couple, and they result in a net torque,
but zero net linear force. When you turn a bolt with a wrench, what you
are really doing is supplying two or more contact forces. The direction and
lever arms of these contact forces are coordinated in a circular pattern to
produce torque, but (nearly) zero net linear force.
In a digital simulation, torques can come from multiple sources. One
common source is an applied (linear) force at some lever arm, with collisions
being the most common source of torques of all. An impulsive force ap-
plied to an object can result in an angular impulse (also known as impulsive
torque). Similar to a linear impulse, an angular impulse is an instantaneous
change in angular momentum, and we can think of this as the result of a
large torque acting for a small duration. We might also instruct the physics
engine to automatically apply torques (perhaps limited to some maximum
magnitude) on an object in order to enforce some angular constraint. Angu-
lar springs and motors are examples of this. Finally, we might have a reason
to add a torque at will to any object without there being any corresponding
linear force.
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