Greenwood press

112
ROTATIONS
Tessellation of lizard tiles based on
rotations for an outdoor patio.
The gears of a bicycle rotate and
latch onto the chain to help propel
the bicycle forward when force is
applied to the pedals.

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rate of approximately 1,037 miles per hour, because these objects travel 2
2π(3,963)
miles in twenty-four hours. The angular rate of objects in circular motion is the
circular distance divided by the time to travel that distance. If a person is stand-
ing away from the equator, then his or her angular rate is 
2π•3963•cos θ
24
, where 
θ
is the latitudinal angle of the city. For example, if a person is standing at 60°N
latitude, then he or she will only be half as far from the earth’s axis of rotation,
because cos 60° is one-half. Then this person will only be moving half as fast
around the earth. People actually do not feel like they are moving faster at dif-
ferent parts of the world because everything else is moving at the same rate. You
feel differences in motion when something else is moving faster or slower than
your motion.
Rocket launches take advantage of the earth’s rotational velocity. The launch-
ed aircraft takes off towards the east—the same direction as the rotation of the
earth—giving it an extra boost once it is airborne. Also, launches in the United
States are at Cape Canaveral, Florida, which is closer to the equator than most
other cities in the country. Since it is farther from the earth’s axis of rotation than
many other U.S. cities, the earth’s rotation will be more supportive at that loca-
tion by giving it almost the best possible additional speed as it leaves the earth’s
atmosphere.
online sources for further exploration
Applications of rotations
astronomy&PageName=rotation>
Bicycle gears


Image rotation

Mathematical art of M. C. Escher

Relative motion—rotation and the motion of the moon

Rotations on a sphere