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ANGULAR AND LINEAR SPEEDS
The relationship between radians or degrees of arc and the distances and sizes of objects can be extended to measure speeds as well. If a distant object moves a certain amount of arc in a certain amount of time, we can relate that to how fast it's going in a straight line if we know the distance. If an object is distance r away from us, then it would travel a distance 2?r if it went all the way around us at that distance. (It's tracing out the circumference of a circle with radius r.) It would also travel 360 degrees, or 2? radians, of arc during that circuit. This is how an angular speed (or distance) can be used to compute a linear speed (or distance). |