Richmond Redux: Relative Velocity

NOTE: Some clarifications added 1:00 p.m. 4/30/12. Thanks to all the commenters, especially @nateryan!

I think Dave Moody did a good job breaking things down. The situation is confounded because there were so many different complications. Who from NASCAR is duly authorized to tell a spotter/crew chief/driver their position? Is it the team’s responsibility to make sure they are lined up the right place or NASCAR’s?  Should NASCAR have held off another lap to make sure that the teams knew what was going on?

The only thing this blog attempts to show is that one should never accept what one sees without questioning it because there are often explanations for why what we think we saw isn’t actually correct.  See my take on technology and data in motorsports.

Of all the things I am mandated to teach in intro physics, the problem where you are swimming across a river and there is a current and you have to figure out at what angle you swim so that you counteract the current and go directly across the water is my absolute least favorite.  I am hard pressed to find a case in which my students have cause to need to know how to do this.

Richmond may have given me a new way of teaching the importance of relative motion.  Although the magnitude of the speed does have an effect on interest, when you come down to it, the crux of racing is whether Car A is running faster than Car B.  It doesn’t matter if Car A is running 180 mph and Car B is running 179 mph, or if Car A is running 150 mph and Car B is running 149 mph.  You win because you are faster than the other car.

Although the restart controversy regarding the 14 and the 99 seems to be more a matter of a communications screw up (both cars claim they were told they were P1), it raises an interesting issue in terms of what we perceive vs. what actually is.  Even sat at a train crossing and had the momentary feeling that the train was standing still and you were moving sideways? Here’s a series of animations I put together really quickly. See if they do the job.

Take a look at the video below and decide which ball is accelerating and which ball is moving at constant speed.

Clearly, the blue ball is accelerating and the yellow ball is moving at constant speed. You can see this more clearly by marking the ball every ten frames, as I’ve done below. Exact same motion, but with markers:

The hallmark of acceleration is that the distance traveled over the same time interval increases. See how the blue balls are more and more spaced apart? That’s acceleration in a nutshell.
Now try this one: Which ball is accelerating this time?

The yellow one, right? Let’s try it again with the markers.

You can see from this that the yellow ball was actually moving at constant speed. The blue ball was decelerating. Because the 14 spun its wheels, it was not accelerating and that made the 99 look like it was accelerating even faster. If you had a frame-by-frame video of the actual restart, you could do the exact same type of analysis with the actual cars and settle for sure whether the 99 was accelerating prior to the starting box.

We judge things by how they look relative to other things. To be a good judge of relative motion, you have to reference your observations to something fixed – like the lines on the animation, or a track wall, or something that isn’t also moving.

This simple demonstration isn’t meant to call into question whether the penalty was right, or who screwed up – just to make people realize that what you see isn’t always what happened.