The National Weather Service does a very useful thing for people who live in an area expexted to experience severe weather danger. I have a little Firefox app in my browser that links to the NWS and advises me of the current conditions and forecast for the next few days, and as part of its mechanical duties it advises me of the various severe weather alerts that happen. They’re popping up at the rate of several times per week now, when the sky is a beautiful crystal blue. Why? Severe heat. Welcome to the southern summer!
I regret to say that I have an advisory of my own: a travel alert. I’m going to be on the road until Friday(ish) and thus posting might be sporadic or nonexistent. The latter is unlikely, I should be able to get at least a couple days in this week. But if not don’t worry. I’m not joining the ranks of the celebrity death outbreak.* Well I’m not a celebrity either, but I’m going to try to avoid the death bit too.
And since I’m on the road, I want to kick off the trip with a driving-related physics fact that few in my classes believe when I tell them. On a smoothly rolling wheel, the point in contact with the ground is stationary. It ain’t moving, no matter how fast the wheel is turning.
Why? The easy answer is that if it were, it would be skidding. A more meaningful answer is that a rolling wheel is really the combination of two motions: circular spinning and linear translation. For a wheel whose center is moving forward at velocity v, the wheel clearly must be spinning such that the points on its rim are also moving at v. The rolling itself makes the points on the top of the wheel spin in the forward direction at speed v, and the points on the bottom are obviously going in the opposite direction, velocity -v.
Add the overall forward speed v, and -v + v = 0 for the bottom of the wheel. You might not believe me, so let’s do the experimentalist thing and actually watch one in action. This nice and much more mathematically complete web explanation has the video.
Not surprising when you think about it, but maybe a little surprising before you think about it.
*Honestly it’s Billy Mays whose death actually managed to make me legitimately a bit sad. Go figure.