University of California physicist, Dmitri Krioukov had a problem. He knew he hadn’t run that stop sign, even though the officer who pulled him over insisted he’d seen him do so. At stake was a $400 traffic ticket… What to do? In oder to beat the rap there were two important questions Krioukov had to answer:
1. Why did the police officer believer that he’d seen him run the stop sign?
2. How could Krioukov prove that he hadn’t done so, despite the officer’s insistence?
To answer these questions convincingly, Krioukov published a scientific paper, illustrating the problem with the officer’s observation. As summarized by PhysicsCentral.com:
When Krioukov drove toward the stop sign the police officer was approximating Krioukov’s angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.
Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when they finally reach us. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.
In Krioukov’s case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer’s perspective.
Combined with the police officer’s momentarily obstructed view, an ill-timed sneeze from Dr. Krioukov and some fancy manta, this explanation was enough to convoke a judge the the officer was wrong in his initial determination that Krioukov hadn’t made the appropriate stop at the intersection.
So stay in school kids. Knowledge is power!