What Are Centrifugal & Centripetal Forces?


You probably have had unpleasant sensations when the car in which you are driving was entering a steep turn. It seemed that now you will be thrown to the side of the road. And if you recall the laws of Newton’s mechanics, it turns out that if you were literally pushed into the door, then some force acted on you. It is usually called “centrifugal force”. It is because of the centrifugal force so breathtaking on the sharp turns when this force pushes you to the side of the car. (Incidentally, this term, derived from the Latin words centrum (“center”) and (“running”), introduced into the scientific use in 1689 by Isaac Newton.)

To the outside observer, however, everything will be represented differently. When the car lays the turn, the observer will consider that you simply continue the straight-line movement, as anybody does which no external force acts on; and the car deviates from a straight trajectory. This observer will seem that this is not pressing you to the door of the car, but, conversely, the door of the car starts to crush you.

However, there is no contradiction between these two points of view. In both reference frames, events are described identically and the same equations are used for this description. The only difference is the interpretation of what happens by the external and internal observer. In this sense, the centrifugal force resembles the Coriolis force ( see Coriolis Effect ), which also acts in rotating frames of reference.

Since not all observers see the action of this force, physicists often call the centrifugal force a fictitious force or pseudo- force. However, it seems to me that such an interpretation can be misleading. In the end, it can hardly be called a fictitious force, which palpably pushes you to the door of the car. Simply the whole point is that, continuing to move by inertia, your body tends to maintain a straight line of motion, while the car evades it and because of this presses on you.

To illustrate the equivalence of two descriptions of centrifugal force, let’s practice a little in mathematics. The body moving at a constant velocity along the circumference, moves with acceleration, as it changes direction all the time. This acceleration is v 2 / r, where v is the velocity, and r is the radius of the circle. Accordingly, an observer in a circumferentially moving frame will experience a centrifugal force equal to mv 2 / r.

Now let’s generalize what has been said: anybody moving along a curved trajectory, whether it is a passenger in a car in a bend, a ball on a string that you unwrap above your head, or Earth in orbit around the Sun, experiences the action of a force that is caused by the pressure of the car door, the tension of the rope or the gravitational pull of the Sun. We call this effect the F . From the point of view of who is in the rotating frame of reference, the body does not move. This means that the internal force F is balanced by the external centrifugal force:

F = mv 2 / r

However, from the viewpoint of an observer outside the rotating reference frame, the body (you, the ball, the Earth) moves at uniformly accelerated speed under the influence of an external force. According to the second law of Newtonian mechanics, the relation between force and acceleration, in this case, is F = ma. Substituting in this equation the acceleration formula for a body moving along a circle, we get:

F = ma = mv 2 / r

But by the same token, we obtained exactly the equation for the observer in the rotating reference frame. Hence, both observers come to identical results relative to the magnitude of the acting force, although they proceed from different premises.

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