-Barbara Buatois set the world's cycling speed record in 2010, on a straight and flat road in Nevada. She travelled a distance of 200m, and was recorded to be traveling at an average speed of 121.81 km/hr, or 33.836 m/s. So, what was her angular velocity and how long did it take for one revolution of her back wheel (the one being powered by the gears)? How does this compare to an average cyclist's speed, just to put things in perspective?
Barbara's world record setting speed! (she's biking enclosed in a covering that probably reduces air resistance)
-I found that a typical diameter of a racing bike's wheel to be 29 inches (.74 m), meaning the radius was .37m. Looking at her bike you can see that her back wheel is probably around this size, but her front wheel is a lot smaller. We will only be paying attention to the back wheel here, because this is the wheel being powered by her pedaling and therefore her speed originates from this wheel.
ω=(33.836 m/s) / (.37m) = 91 rad/s is her angular velocity (crazy...)
-Finding how long it takes to do one rotation of the tire further shows how fast this woman is moving.
91 rad/s =(2π)/T
T= .069 seconds per revolution (an insanely small amount of time for that wheel to do one full revolution when you think about it...)
-Now, let's compare this to an "average" biker so that we can see the huge difference. Online I found that racing cyclists can hold a speed of about 30mph for short periods of time, but the "average" cycling speed is between 10-20 mph. Therefore, I chose a speed of 15 mph to compare Barbara to. 15 mph is equal to 6.7 m/s.
ω=(6.7 m/s) / (.37m) = 18 rad/s
18 rad/s = (2π)/T
T= .35 seconds per revolution
-There is obviously a huge difference in these two cyclist's angular speed and period of the wheel. Just some other fun facts:
-The top of Barbara's wheel (v=2ωr) was moving at 67.67 m/s, or 151.4 mph.
-Barbara has also set a world record in the distance biked in an hour- with 84.0204 km in one hour flat. Average velocity = (Δx/time), so that's an average velocity of 23.4 m/s, or 52.3 mph!!!