The Quarter That Defied Physics

Recently, a video landed in my inbox, sent in by a reader who observed what seemed to be an impossible phenomenon: He spun a quarter and, in flat defiance of the law of conservation of angular momentum, the thing spontaneously switched the direction that it was spinning halfway through.

Take a look for yourself and see if you can figure out what’s going on:

Stumped? I was at first, but—as so often happens with these things—sometimes all it takes is a fresh pair of eyes. When I called over my coworker “Laser” James Roche to look at it, he immediately had the answer. It’s not a trick quarter, or anything to do with the table—it’s a camera trick, albeit one so convincing it even fooled the person who took the video.
Whether it’s an old-school film reel or a digital .GIF file, a video is just a series of still images displayed one after another, fast enough that our brains string them together to form a coherent scene. The rate at which those still pictures are taken and then displayed is called the frame rate, and it takes only takes a few dozen frames per second (fps) to trick the brain into seeing the series of stills as a movie. 
While that’s a fast enough refresh rate to render most everyday occurrences accurately, it can create weird effects with fast, periodic phenomena—like the spinning of a quarter, or the blades of a fan. If your camera is taking a photo of the fan 20 times a second, and the fan is making 20 turns per second, it’s going to appear stationary in your video. And if it’s a four-bladed fan with identical blades, you’ll get the same effect if it’s turning 5 or 10 times a second, because your video will consist of images all taken a quarter-turn or a half-turn apart, respectively.
In the video, the quarter is spinning rapidly, appearing as a blur at first—even with the camera’s slow-motion function engaged. Soon, it becomes easier to make out, giving the impression that it’s slowed down—and it has, but not quite as much as it appears. The quarter is still spinning faster than the camera can capture, but as it slows down, its rotation rate approaches the camera’s frame rate. If your camera takes images 20 times per second and the quarter is rotating 20 times per second, it’ll appear to stand straight up on its edge. If the quarter is rotating 21 times per second, then each image will have the quarter offset very slightly from where it was when the last image was taken, and it’ll seem to be rotating very, very slowly. The same goes for 19 rotations per second, only each frame would show the quarter having almost made it back around to where it was when the previous image was taken, also giving the impression that it’s rotating very slowly—only now, in reverse.
Knowing this, it’s easy to see what’s happening in the video. As the quarter slows down thanks to friction and air resistance, its rotation rate approaches the camera’s frame rate, matching it about 11 seconds in—when the quarter seems to stand still on edge for a moment. As the quarter’s angular velocity drops further, it seems to start rotating the opposite direction, creating the confusing effect that appears to violate the laws of physics.

Similar trickery is at work with this helicopter that flies without spinning its blades.

This kind of thing happens with just about any periodic phenomenon, not just rotation. Combined with the rolling shutter method of image capture, it can create some truly mind-blowing visuals when things like heavy bass or guitar strings.
Stephen Skolnick

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