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

• fisico30
In summary, the centripetal force is a perpendicular force to the velocity of an object that maintains its trajectory, without causing changes in kinetic energy. In the situation described, the tension in the rope acts as the centripetal force on object1, while object1's inertia causes the tension in the rope that is then transmitted to object2. The object1 is not pulled towards the center of the table because it is rotating at the right speed, and its inertia causes it to maintain its straight line motion, resulting in a circular path. This is similar to the circular orbits of planets where the objects are actually falling towards the center, but the radial distance they fall is compensated by the distance traveled along the tangent, keeping them at a fixed distance
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

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.

## 1. What is centripetal force?

Centripetal force is the force that acts on an object moving in a curved path, directed towards the center of the curve. It keeps the object moving in a circular motion and prevents it from flying off in a straight line.

## 2. How is centripetal force different from centrifugal force?

Centripetal force and centrifugal force are often confused, but they are actually two different concepts. Centripetal force is the inward force that keeps an object moving in a circular motion, while centrifugal force is the outward force that appears to push an object away from the center of rotation. Centrifugal force is actually a perceived force and does not actually exist.

## 3. What are some examples of centripetal force in everyday life?

Some examples of centripetal force in everyday life include the force that keeps a car moving around a curve, the force that keeps water inside a spinning bucket, and the force that keeps planets orbiting around the sun.

## 4. How is centripetal force calculated?

The formula for calculating centripetal force is F = mv²/r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the curve. This formula shows that the greater the mass and velocity of the object, or the smaller the radius, the greater the centripetal force needed to keep it moving in a circular path.

## 5. Can centripetal force be greater than the weight of an object?

Yes, centripetal force can be greater than the weight of an object. This is because centripetal force is dependent on the mass and velocity of the object, while weight is dependent on the mass and the acceleration due to gravity. So, an object can experience a greater centripetal force while still having the same weight.

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