Speed of a Rotating DiscDate: 03/01/98 at 04:13:28 From: Justin Yeo Subject: Re: Average speed Dear Doctor Math, I have a problem with this question: You have a compact disc rotating at a constant speed. The outer-most edge of the compact disc is rotating at, say, 20 km/h. Thus, the inner-most edge of a compact disc is also rotating at 20km/h. It is easily noticeable that the outer edge is travelling a longer distance than the inner edge, but if this is true, then the speeds should be different (the outer edge should spin faster, as it has to cover more distance in the same period of time). But saying that the outer edge spins at a higher rate is also wrong. I tried this out with a paper disc and made two markings (one on the inner edge and one on the outer edge) on a straight line, and after spinning the disc for a while, the markings were still in line with each other. If one of the edges had spun faster than the other, the paper would have been ripped to pieces! This simple experiment proves that the outer edge spins no faster than the inner edge. Dr Math, this question seems unsolvable to me. I know that there must be a mathematical explanation, but what? Date: 03/01/98 at 08:43:40 From: Doctor Jerry Subject: Re: Average speed Hi Justin Yeo, Maybe you are mixing two kinds of speeds. Every point on the disk has the same angular speed, usually measured in radians per second. If the disk is turning at 10 rpm, then its angular speed is 10 rev 2*pi 1 min ------ * -------- * -------- = (pi/30) radians/sec 1 min 1 rev 60 sec The linear speeds of points on the disk depend upon how far they are from the center. You need the fact that the length s of the arc of a sector with central angle w (radians) in a circle of radius a is s = a * w In one second, the central angle will have increased by pi/30 radians. A point 2cm from the center will have moved 2*(pi/30) cm; a point 4 cm from the center will have moved 4*(pi/30). The relation between linear speed and angular speed is that linear speed = a* angular speed. -Doctor Jerry, The Math Forum Check out our web site http://mathforum.org/dr.math/ |
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