Understanding Centripetal Force: Solving for Tension

[i.mehrzad]

I am thoroughly confused about centripetal force.

I was doing this problem myself and when looked at the solution i was fairly confused.

The problem was like this.

There is a thread which is hinged to a pole and the pole is rotating with an angular velocity of 'w'. The rope has got finite mass m. What is the tension of the rope as a function of 'r' which is the distance fro the pole aloong the rope.

In the solution i had this problem.

They considered a diffrential length dr which is situated at a distance r from the pole.

Towards the right of dr the tension is pointing to to the right, and to the left of dr the tension is pointing to the left.

I wanted to know that why is there a difference in the direction of tension. When the cause of both is the same, that is centripetal accelaration.

 

[Doc Al]

Think of the tension as being a condition of the thread, not just "a force". The bonds of the thread are being stretched. That tension will create forces on each end of a segment of the thread--often we loosely refer to the force created by tension as just "tension".

A rope or thread under tension must have an outward force exerted on each end (by whatever is pulling the rope taut), and it will exert an inward force at each end (per Newton's 3rd law) on whatever is pulling it taut. To find the force on any particular segment of rope, consider the forces acting on that segment: At the right end of the segment, the adjacent material pulls the thread to the right; at the left end, to the left.

Another way of describing it that might help: Think of the rope as being two pieces tied together. If the rope is under tension, the left half must pull the right half to the left; conversely, the right half must pull the left half to the right. Make sense?