What is the angular speel of a 19-in. diameter bicycle wheel if the bicycle if traveling at 29 ft/s?

Speed = R w

R = 9.5 inch
Speed = 29*12 = 348 inch/s
w = angular speed = 348/9.5 = ? radians/s

Speed and R must both use the same length units when calculating w. I chose to use inches

To find the angular speed, we need to know the linear speed of the bicycle and the radius of the wheel.

First, let's convert the diameter of the wheel from inches to feet:

Diameter = 19 inches
Radius = Diameter / 2 = 19 inches / 2 = 9.5 inches

Converting inches to feet:
Radius = 9.5 inches * (1 ft / 12 inches) = 0.7917 ft

Now, we can use the linear speed of the bicycle and the radius of the wheel to find the angular speed. The linear speed is given as 29 ft/s.

The formula to relate linear speed (v) and angular speed (ω) is:
v = ω * r

Rearranging the formula to solve for ω:
ω = v / r

Substituting the values we have:
ω = 29 ft/s / 0.7917 ft

Calculating the answer:
ω ≈ 36.675 rad/s

Therefore, the approximate angular speed of a 19-inch diameter bicycle wheel when the bicycle is traveling at 29 ft/s is approximately 36.675 rad/s.