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The London Eye is a large ferris wheel. Each sealed and air-conditioned passenger capsule holds about 25 passengers. The diameter of the wheel is 135 m, and the wheel takes about half an hour to complete one revolution.
a) Determine the exact angle, in radians, that a passenger will travel in 5 min.
b) How far does a passenger travel in 5 min.?
c) How long would it take a passenger to travel 2 radians?
d) What is the angular velocity of a passenger, in radians per second?
e) What is the angular velocity of a passenger, in degrees per second?
Since you state that the wheel takes about half an hour to complete one rotation, how can you expect an exact angle in a)
a) in 30 min it rotates 2pi radians
in 1 min it rotates 2pi/30 radians
in 5 min it rotates 5(2pi/30) or pi/3 radians
b) find the circumference (C) of the wheel, that will tell you how far a person travels in one rotation.
Now, what fraction of 30 minutes is 5 minutes ?
c) set up a ration:
C/(2pi) = x/2 , solve for x
d) it moves at 2pi radians every 30 min
= 2pi/30 rad/min
= 2pi/(30*60) rad/sec
= pi/900 radians/sec
e) same thing, use 360º instead of 2pi