Uniform Circular Motion of Swinging Objects

[Amenable Me]

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.

 

[Simon Bridge]

How does one derive the tension of the rope only given the angle, not the period or velocity?

You also need the mass ... and you draw a free-body diagram.

Is the tension of a non-vertical rope depend entirely upon the vertical forces acting upon it?

No - it depends on the radial forces acting on it.

If, say, gravity is the only force acting, then the tension will provide a net unbalanced force pointing perpendicular to the rope (in the direction of the acceleration).
You should realize that, when something is swinging, the circular motion is not uniform - there is also a tangential acceleration.

It would help if you can answer it with physics and not math.

I hear you - but bear in mind that math is the language of physics.