2008 AAPT High School Physics Photo Contest
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Named by Galileo in 1599, a cycloid is the path that a point on the edge of a circular wheel follows as the wheel moves along a straight line. A cycloid is also the solution to the Brachistochrone problem (the curve between two points that is covered by an object in the least amount of time, starting with zero speed, ignoring friction, and acting under constant gravity.) Its parametric equation, assuming that the cycloid is starting at the origin, is x=r(t-sin(t)), y=r(1-cos(t)). This photo is a long exposure taken at night. I attached an LED to the edge of the tire, opened the camera's shutter, then had my dad drive the vehicle in a straight line until it reached where I knew the edge of the frame was and stop. In order for the vehicle to show up, I had to light up the vehicle for about 10 seconds with a spotlight.