A Ferris wheel at a carnival has a diameter of 58 feet. Suppose a passenger is traveling at 9 miles per hour. (A useful fact:.) (a) Find the angular speed of the wheel in radians per minute. (b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.) Do not round any intermediate computations, and round your answer to the nearest whole number.

a) 27.2 rad/min

b) 260 rev/h

Explanation:

The passenger is traveling at 9 mph, this is the tangential speed.

The relation between tangential speed and angular speed is:

v = r * w

Where

v: tangential speed

r: radius

w: angular speed

Also, the radius is

r = d/2

d is the diameter

Therefore:

v = (d * w) / 2

Rearranging:

w = 2*v/d

w = (2*9 mile/h) / (58 feet)

We need to convert the feet to miles

w = (2*9 mile/h) / (0.011 miles) = 1636 rad/h

We divide this by 60 to get it in radians per minute

w = 1636/60 = 27.2 rad/min

Now the angular speed is in radians, to get revolutions we have to divide by 2π

n = v / (π*d)

n = (9 mile/h) / (π*0.011 mile) = 260 rev/h