What Causes Tension in a Whirling Rope?

[amiras]

Homework Statement

A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity ω.

Homework Equations

At a point on the rope a distance r from the end that is held what is the tension F?

The Attempt at a Solution

Clearly the Newtons second law in radial form should be used. I do not really understand what causes the tension. Imagine a point on the rope a distance r from the end that is held. At this point there is a force directed to the center of the circle because of centripetal acceleration, also the rest of the rope accelerates away from the center of the circle and tends to pull the point?

 

[mfb]

At any point on the rope, the part outside has to be kept in a circular motion: this requires a force, identical to the tension at that point.