In the circular motion, What does it mean by this equation s = r.θ?
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Aug 9, 2018 #2 Luke Velie 7 0 S=rø is the formula for arc length, or angular displacement (ø rad). R is the radius Ø is the angle measure in radians.
S=rø is the formula for arc length, or angular displacement (ø rad). R is the radius Ø is the angle measure in radians.
Aug 9, 2018 #3 Delta2 Homework Helper Insights Author Gold Member 3,563 1,376 The scheme is not perfect but I think you get the idea... If you want to know how this equation is proved: Due to symmetry of the circle we can assume that the arc length ##s## will be directly proportional to the angle ##\theta##. So it will be ##s=k\theta## (1) for some constant k. But we know for angle ##2\pi## corresponds arc length ##2\pi r##. So if we apply equation (1) for those pair of data we get ##2\pi r=k (2\pi)## from which we can deduce that the constant k is actually the radius of the circle, ##k=r##. Attachments arctheta.png 10.7 KB Views: 476 Last edited: Aug 9, 2018
The scheme is not perfect but I think you get the idea... If you want to know how this equation is proved: Due to symmetry of the circle we can assume that the arc length ##s## will be directly proportional to the angle ##\theta##. So it will be ##s=k\theta## (1) for some constant k. But we know for angle ##2\pi## corresponds arc length ##2\pi r##. So if we apply equation (1) for those pair of data we get ##2\pi r=k (2\pi)## from which we can deduce that the constant k is actually the radius of the circle, ##k=r##.