# Why do we use the term 'centrifugal force' to calculate net gravitational force?

When an object, orbiting in circular path, experiences the sensation of being thrown outward away from the centre of circle. We often think that an outward force or centrifugal force is responsible for this trend. But it is wrong idea. Inertia is responsible for this. Since earth rotates around its axis, an object standing on the surface of earth rotates with earth. We say that it affect the downward force that object feels while standing on the surface of earth, and to calculate the net value of attraction force between earth and object we subtract the value of centrifugal force from the weight of that object. This is because centrifugal force pulls this object outward, and the value of centrifugal force equals to that of centripetal force. But we know that centrifugal force is not responsible for the sensation of being thrown from the centre of circle. So why, in the case of effect of earth's rotation on value of net gravitational force, do we think that centrifugal force wants to pull the object to outward?

• It's just the term used for the 'virtual' force that has to be included when considering force balances in a rotating (non-inertial) reference frame. What's wrong with it? Jan 18, 2015 at 14:03

I believe it derives from the Latin words centrum (meaning 'center') and fugere (meaning 'to flee'). It is the term used for a virtual inertial force that is apparent when considering force balances in a rotating (non-inertial) reference frame. This virtual force would appear to make objects in a rotating frame want to move outwards, if there are no other forces acting upon them.

The problem arises from jumping between two different frames of reference in describing the "motion" of the object in question, and applying Newton's Laws of Motion.

If we make the wiser choice, we choose a frame of reference in which the earth is rotating once every day. Then the object is rotating in a circle, and we need to assign some of the forces we find to the job of maintaining this accelerated motion. We call the force the centripetal force. Note that it is not a source of a force; it is a task we assign to some real force: gravity acting on a satellite, the tension of a string swinging a rock in a circle, the friction between the tires and the road as a car rounds a curve, etc.

We can also observe that, apart from this acceleration, the object is not accelerating in any other way; we know that all the forces we find must result in just this centripetal acceleration.

If we then look at this object, we discover that there are only two real forces acting on the object: the force of gravity, and the force of reaction of the ground on the object. We can then proceed to measure various forces and calculate others, knowing that all these real forces must add up the centripetal force. We never mention or even think the words centrifugal force; if we do, our friends point at us and laugh.

Imagine that you are doing the books for a business, and you are told that the business must make a profit of 1,000,000. You don't then put down that million dollars as a source of money. Instead, you look at all the real cash flows: purchases, taxes, sales, etc. knowing that you need to find values for all the revenues and expenses (positive and negative) such that the total is one million dollars.

A poorer (in my opinion) choice of frame of reference is to take the earth as non-rotating. In this frame, the object on the surface of the earth is completely at rest, and thus Newton says that all the forces acting on it must add up to zero. There is no need to assign any forces to the task of exerting a centripetal force, because the object is not rotating.

But before we start looking at the real forces, we must make an adjustment. We somehow know that our frame of reference is rotating (relative to what??) and thus we must create some new, invisible forces which are acting on the object, and which depend on (among other things) the rate of rotation of the frame of reference. The centrifugal force is one of these. If we include this centrifugal force with the force of gravity and the force of the ground, and require that the total be zero, we can do the same calculations, with the same results as in the rotating earth case.