# Is centrifugal force equal in magnitude to the centripetal force in the frame of a body undergoing circular motion?

I was working out the minimum tangential velocity required for a swing to complete a full revolution and assumed the centripetal force is equal to the centrifugal force, so that I could set the weight force equal to the formula for centripetal (i.e. net force 0 at the top so swing won't fall). I'm pretty sure the answer is correct but doubt my reasoning.

## 2 Answers

If you set your reference frame to be fixed to the swing (let's call the origin the pivot point of the swing), you are now dealing with a rotating reference frame.

In a rotating reference frame, all objects observe a centrifugal force that pulls them outwards from the origin. For any stationary object in your rotating reference frame (the seat on the swing), the sum of forces must be equal to 0. The name we've ascribed to whatever force is equal and opposite to the centrifugal force is "centripetal force".

In your case, this magical "centripetal force" is some combination of the tension in the swing's chain/rope and the force due to gravity acting on whatever is in the seat of the swing.

To answer your question directly: Your thinking appears correct, but beware that centripetal force is only equal in magnitude to centrifugal force when the object it is acting on is stationary in your rotating frame. Furthermore, this case is what defines "centripetal force" in the first place.

And don't say "weight force" unless you're explicitly describing the apparent weight of an object (i.e. what the object "feels"; e.g. the weight on the seat of the swing). It can be confused with the weight of an object (force solely attributed to gravity).

Your reasoning should be improved. In an inertial system there are no centrifugal force. You may in that system speak about a centripetal force, which is not a real force but an expression for how much net force is needed for the object to perform a circular motion. You probably mean that the expression for the centripetal force should be equal to the physical force at hand, the weight force.

• Centripetal force is a real force. Centrifugal force is an apparent force. – wgrenard Aug 16 '14 at 20:56
• wgrenad - I try to tell students that the expression for the centripetal force $F_c=mv^2/r$ is not a real force, but rather an expression for how large force perpendicular to the orbit is needed. There is always som real force that create this, e.g. from a string or gravitational force. – Per Arve Oct 26 '14 at 17:41