# A question about central forces

Will a force pointing towards a fixed point but having constant magnitude (and not depending on the distance from fixed point) be a central force?

• What's your definition of "central force", and what trouble do you have in applying it here? – ACuriousMind Oct 7 '17 at 11:25
• – Qmechanic Oct 7 '17 at 13:42
• Thanks for reply! Definition is " a central force on an object is a force whose magnitude only depends on the distance r of the object from the origin, and is directed along the line joining them." So should the magnitude necessarily depend on distance or if it depends it should be the distance only. This is my concern – Umang Oct 7 '17 at 15:37

In classical mechanics, a central force on an object is a force whose magnitude only depends on the distance $r$ of the object from the origin, and is directed along the line joining them.

In short, the forces acting upon the line joining the centers of two bodies are called central forces.

The stress is on the distance of the body from the origin, and the force has to be directed along the line joining the origin and the body.

So, in your example, the force is a central force.

Examples of central force are Coloumbic force, and Gravitational force.

Later on, you might encounter a term, central potential, which is simply the potential depending on the distance of a body from the origin.

Anything central means that only depends on distance from origin.

In the above picture, the distance of the body at P from O is $r$. As the force $F_{att}$ acts along the line joining the body and the origin, that is the position vector, the force is a central force.

• Thanks for the reply. So the magnitude should necessarily depend on the distance, is that what is implied by "only on distance" OR is it if it depends it should be the distance? – Umang Oct 7 '17 at 15:40
• Either way. If the force varies, it should only depends on distance. – Wrichik Basu Oct 7 '17 at 15:41
• So a constant magnitude force directed towards a fixed point would be a central force as it's magnitude is not depending on anything? I am not clear about this specific thing. And also its my first post :) – Umang Oct 7 '17 at 15:46
• @Umang yes, it would be central if it works along the direction I've stated. – Wrichik Basu Oct 7 '17 at 15:47
• Great. If it has helped you, you can accept the answer by clicking on the tick just below the up down vote buttons. However, please note that I'm not forcing you, I just want that in future, others shouldn't think that this question was unanswered. :-) @Umang – Wrichik Basu Oct 7 '17 at 16:28