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**1. Homework Statement**

Given a rope with a constant length L, and a mass M.

The rope is connected in one side, and moving with angular velocity on a frictionless surface.

What is the tension along the rope?

Hint:

Look at a small mass element of the rope and consider the forces acting on it, and therefore arrive at a differential equation.

**2. Homework Equations**

**3. The Attempt at a Solution**

Im a bit new to this way of looking at problems by looking at them in very small parts, but it does look beautiful, so any help with getting me acquainted with it will be much appreciated! I do have the math needed, but not the intuition of how to break a problem to its infi parts.

So, since an angular velocity is mentioned, I obviously thought about a circular movement. The rope is moving along the circumference of a circle. Which means a force F must be applied to its connected end, and the force pointing to the center of the circle.

On the other hand, when I look at a very small element of rope, its a particle moving in circular motion. But what are the forces acting on it? F would act only at the connected end, wouldnt it? So the force acting on the particle is T1 towards one side tangential to the circle, and T2 towards the other tangential side? How does that explain it's circular motion? (he must have some force towards the center, not on the tangential axis)

What force causes the circular motion when looking at a very small mass particle?

Any help would be much appreciated!