Understanding Centripetal Force: The Case of Rotating Objects on a Table

[fisico30]

Hello Forum,
I think I understand what the centripetal force does: it is a force perpendicular to the velocity of the object, a force that does not cause changes in kinetic energy but only modifies the trajectory.

I am not clear on this specific situation: object1 is rotating on a table. It is also connected through a rope to another object2 that is hanging just under the center of the table. The tension in the string supports the weight of object2. Object2 is supported as long as object 1 is rotating at the right speed.
Here the question: object1 has some inertia and tries to move along the tangent direction, along a straight path.
The tension T in the rope is the centripetal force on object1 and points radially inward. At the same time, object1 exerts a force (by action-reaction) on the rope itself pointing radially outward. So the inertia of object 1, its tendency to maintain its straight line motion causes the tension in the rope that is then transmitted via the rope to the hanging object2.

Why is object1 not being pulled toward the center of the table while it rotates?
In the centripetal force examples of free-falling objects trapped in the gravitational field of a planet, the objects are actually falling and moving towards the center but the radial distance they fall toward the center is compensated by the distance traveled along the tangent: the object remains at a fixed distance from the center.

In the case of the rotating object1 on the table, the object1 is not actually moving at all toward the center, or is it...?

thanks for any conceptual clarification,
fisico30

 

[Matterwave]

If the trajectory is perfectly circular, and there are no frictional forces, and the velocity is calibrated perfectly, then object 1 will not move towards the center.

This is also true for circular orbits of planets.