Centripetal Motion Homework: Mass of String/Spring Effect

[bjgawp]

Homework Statement

When solving problems involving centripetal motion, say rotating a string/spring with an object attached to it, without taking into account of the mass of the string/spring. What effect would it have if we DID take it into account?

Homework Equations

The Attempt at a Solution

If we were to twirl the mass in a horizontal circle, I would think that the weight of the string/spring would lower the height of the circular path, like a conical pendulum - affecting the radius of its path. Am I going in the right direction .. ?

 

[Shooting Star]

That's right. Think of a very heavy rod replacing the string. For the same energy, it would revolve at a lower height.

 

[Moetasim]

Your thinking is correct. Taking into account the mass of the string/spring would affect the radius of the circular path. This is because the string/spring has its own mass and therefore, has its own inertia. This inertia must be overcome in order for the object attached to it to move in a circular path. As a result, the radius of the circular path would be slightly smaller than if we did not take into account the mass of the string/spring. This effect would be more significant for objects with larger masses attached to the string/spring. Additionally, the tension in the string/spring would also increase due to the added mass, which would affect the centripetal force acting on the object. Overall, taking into account the mass of the string/spring would provide a more accurate and precise solution to problems involving centripetal motion.