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Angular position
The first is the angular position, conventionally
denoted by , as in Figure 5.1. This is
the angle at a particular instant in time that the object
makes with respect to some fixed reference axis. This angle
may be measured in degrees, although in some instances it is
more convenient to express it in a unit called radians.
A radian is defined such that 2
radians represents one
complete revolution (360^{o}). The conversion is therefore
1 radian = (360/2)^{o}. Since
is approximately
3.14, this gives about 57^{o} per radian. Radians have special
geometrical and physical significance, because for an object going
in a circle, the distance traveled by the object (i.e. arc length)
is precisely equal to the angular displacement in radians times
the radius of the circle.
One of the reasons that the description of circular motion in terms of
angular displacement is so useful is that it can be applied to
the motion of
extended, rigid objects rotating about a fixed axis. In particular, if an
object, such as the one shown below, is rotating about an axis through
the point, O, its motion is completely described by the angle
through which any point in the object has rotated about that
axis. This is true because every point in the object must rotate around
the axis the precisely the same number of times per second, otherwise
the object
would break apart, or deform.
Figure 5.2:
Rotation of an extended object about a fixed axis.

Next: Angular velocity
Up: Circular motion
Previous: Circular motion
modtech@theory.uwinnipeg.ca
19990929