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**Unformatted text preview: **volution is 2π radians, so ω = 224radians = 12 hours ,
hours
where, once again, we are using the fact that radians are real numbers and are dimensionless. (For
simplicity’s sake, we are also assuming that we are viewing the rotation of the earth as counterclockwise so ω > 0.) Hence, the linear velocity is
v = 2960 miles · π
miles
≈ 775
12 hours
hour It is worth noting that the quantity 1 revolution in Example 10.1.5 is called the ordinary frequency
24 hours
of the motion and is usually denoted by the variable f . The ordinary frequency is a measure of
how often an object makes a complete cycle of the motion. The fact that ω = 2πf suggests that
ω is also a frequency. Indeed, it is called the angular frequency of the motion. On a related
1
note, the quantity T = f is called the period of the motion and is the amount of time it takes for
the object to complete one cycle of the motion. In the scenario of Example 10.1.5, the period of
the motion is 24 hours, or one day. The concept of frequency and period help frame the equation
v = rω in a new light. That is, if ω is ﬁxed, points which are farther from the center of rotation
need to travel faster to maintain the same angular frequency since they have farther to travel to
make one revolution in one period’s time. The distance of the object to the center of rotation is the
radius of the circle, r, and is the ‘magniﬁcation factor’ which relates ω and v . We will have more to
say about frequ...

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