Radical Rotations

As I looked out my window this morning and saw the snow I couldn't help but look forlornly at my longboard leaning up in a corner of my room. Winter is here and I won't be riding that for quite sometime. But then I started thinking about the fact that a longboard can get going pretty quick even though it has relatively small wheels. That got me thinking, if I'm cruising down the hill how fast are those little wheels spinning?

The speed limit up the hill is fifteen miles per hour and going down Oak drive one can easily hit that because of the slope. This is equal to roughly 6.7 m/s. If the radius of the longboard wheels is 3.25 cm then we can convert these quantities into rotational velocities.

v=15 mph=6.7 m/s

r=3.25 cm=0.0325 m

w=v/r

w=(6.7 m/s)/(0.0325 m)=206 rad/s

We can take this angular velocity and turn it into revolutions per minute by converting our units.

(206 rad/s)(1 rev/2*pi rad)(60 s/1 min)=1967 rev/min

As a comparison: the average car runs at around 2000 rpm when cruising easily down the road. 

In any event, bombing the hill is probably a terrible idea and if we've learned anything from professor Metzler it's that you should ALWAYS wear a helmet.