Answer:
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
