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Note that the x and y components of the torque vector are 0; thus, the torque moment
is pointing directly along the z-axis. The torque vector would be pointing out of the
page of this topic in this case.
In dynamics you need to consider the sum, or total, of all forces acting on an object
separately from the sum of all torques acting on a body. When summing forces, you
simply add, vectorally, all of the forces without regard to their point of application.
However, when summing torques you must take into account the point of application
of the forces to calculate the torques, as shown in the previous example. Then you can
take the vector sum of all torques acting on the body.
When you are considering rigid bodies that are not physically constrained to rotate
about a fixed axis, any force acting through the body's center of mass will not produce
a torque on the body about its center of gravity. In this case, the axis of rotation passes
through the center of mass of the body and the vector r would be 0 (all components 0).
When a force acts through a point on the body some distance away from its center of
mass, a torque on the body will develop, and the angular motion of the body will be
affected. Generally, field forces, which are forces at a distance, are assumed to act
through a body's center of mass; thus, only the body's linear motion will be affected
unless the body is constrained to rotate about a fixed point. Other contact forces, how‐
ever, generally do not act through a body's center of mass (they could but aren't neces‐
sarily assumed to) and tend to affect the body's angular motion as well as its linear
motion.
Summary
As we said earlier, this chapter on forces is your bridge from kinematics to kinetics. Here
you've looked at the major force categories—contact forces and force fields—and some
important specific types of forces. This chapter was meant to give you enough theoretical
background on forces so you can fully appreciate the subject of kinetics that's covered
in the next chapter. In Chapter 15 through Chapter 19 , you'll revisit the subject of forces
from a much more practical point of view when we investigate specific real-life prob‐
lems. We'll also introduce some new specific types of force in those chapters that we
didn't cover here.
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