In video, a rotating wheel can appear to turn in the opposite direction to which
ID: 1915878 • Letter: I
Question
In video, a rotating wheel can appear to turn in the opposite direction to which it is actually turning. As a result, a car moving forward can have its wheels appear to rotate in a manner that should move the car in reverse. This effect is due to what is known as aliasing and the persistence of vision. The degree to which this occurs depends on the speed of rotation and the frame rate of video capture. Consider a wheel with eight uniformly spaced spokes and a radius R = 0.3 m. The wheel is rotating in the clockwise direction (negative angular displacement), which would move the vehicle forward (positive direction), and due to aliasing the wheel has an apparent linear velocity of vapp = -0.785 m/s. In the United States the typical video frame rate is 30 frames/second. Assuming that the car is moving with a constant velocity use this information to a) Derive a general expression for the actual velocity of the car. (Hint: Consider the angular displacemtn of each individual spoke and look for a pattern.Your expression will have a variable n which represents the spoke number.) b) Label the spokes on your wheel and identify which spoke gives an actual speed near 25 m/s. (Note that the actual speed is NOT 25 m/s but is in the vicinity of it.) c) Using the initial speed found in part b, determine the apparent speed of the wheel if the video were recorded using a 25 frame/sec standard.Explanation / Answer
Wheels appear to rotate backwards in movies because of what is called, 'strobe effect'. When filming, the camera actually takes a series of pictures. An example would be:
Imagine you have a spoked wheel rotating at 50 revolutions per second. If the camera is filming at a rate of 50 frames per second (taking 50 individual pictures each second) then the wheel would be in the same position every time the picture was taken. When viewing the film it would appear that the wheel was not moving. Now, slow the wheel down a little bit and it would be slightly behind the position it was in when the previous frame was shot. Now the wheel would appear as if it is rotating backwards because you are not viewing the continuous motion of the wheel, but rather the positions of the wheel every 1/50th of a second. You can see the same effect when looking at a fan turning in a room with Fluorescent lighting. The bulbs flicker at a certain cycle thus causing the illusion.
in other words
This is a stroboscopic effect which happens when you are seing repeated images of the tire. This can happen if you see the tire on film (often 24 frames a second) or on a TV or lit by an AC electric light or any process which regularly breaks up your image of the tire, such as looking through a fan at the tire.
Normally the eye will interpret the sucessesion of rotated images of the tire as the tire rotating because each image has rotated a little further than the previous one.
If the tire is rotating quickly enough that by the time you see the next image of the tire, it has rotated so much that patterns on the tire are slightly backward from the previous image, (for example, maybe it made 99% of a turn), then what you are seeing is exactly the same as it would look if the tire really was moving backwards and so that is what you see.
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