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If you plot the 'y-axis' displacement of a rotating obejcet and the 'y-axis' displacement of a vibrating particle you get exactly the same displacement-time graph. The time axis of that graph could be expressed as the angle (in radians or degrees). In physics the difference in phase of waveforms is usually expressed in radians - 2π radians being equivalent to a full cycle or 360o. Click here to see an animation of the relationship between the rotating radius and the sinusoidal graph produced.
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