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Uniform Circular Motion of Swinging Objects

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I am very confused with a particular aspect of part of my physics curriculum.

Let's say there is an object swinging on a rope swinging in a circular motion. The mass of the object, length of rope, and angle of rope relative to y axis are known.

How does one derive the tension of the rope only given the angle, not the period or velocity? I have seen previous attempts use the weight of the object to determine the tension, but that seem to include all of the forces necessary (centripetal force?). Is the tension of a non-vertical rope depend entirely upon the vertical forces acting upon it?

I would greatly appreciate any help on this. It would help if you can answer it with physics and not math.

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