CENTRIFUGAL FORCE Case 1

Fwall FCentrifugal 2 Fwall = FCentipetal = mv /R

Consider the following situation. A small block (blue) is up against the wall of a rotating platform. This situation is viewed by two observers: one (green) who is on the rotating platform and one (purple) not on the rotating platform. The green observer is in a non‐inertial (accelerated) reference frame and the purple observer is in an inertial (non‐accelerating) reference frame (the Earth!). The green observer notices that if the block is moved away from the wall, it slides back to the wall, and concludes that the block must be in equilibrium (a = 0) under the action of an outward centrifugal force and the inward force the wall exerts on it. This is faulty reasoning resulting from the fact that the green observer is in a rotating reference frame. The purple observer (non‐accelerating) correctly concludes that the block is certainly not in equilibrium because it is moving in a circle and finds that the centripetal force that causes the block to move in a circle is provided by the inward force of the wall.

Case 2

R

Observer on the

ground

object observer

Centrifugal force is a fictitious (i.e., not real) force perceived to act on objects by an observer in an accelerated (i.e., non‐inertial) reference frame. In this example, a car is driving along a straight road with a constant speed v and enters a turn having a radius of curvature R. The driver (observer) maintains constant speed in the turn, but since the turn is ¼ of a circular, the car and the driver undergo a centripetal acceleration. The centripetal acceleration of the car is provided by the friction force on the tires by the road. The centripetal acceleration of the driver is provided by his seat belt. Suppose there is some object resting on the dashboard of the car. As the car drives through the curve, the driver notices that the object appeared to move to the extreme right side of the dashboard and concludes that there must have been an outward force – a centrifugal force that acted radially outward and pushed the object to the right side.

The driver is a non‐inertial observer and invents this fictitious centrifugal force to explain the apparent motion of the object. He also concludes that the object is in equilibrium under the opposing centrifugal force and the force that the side of the car exerts on it.

The observer on the ground is in an inertial reference frame (the earth) and concludes the following. The object, by virtue of its inertia, resists changes in it velocity. To make the turn with the car, some force (real) must be acting to produce the centripetal acceleration required to make it move in a circular path. The only force available for this purpose would be the friction force between it and the dashboard. This friction force must be insufficient to accomplish this and thus the object continues moving in a straight line as any undisturbed object would. So in effect the car slid out from under the object, and the object ends up against the right side of the car which does exert a real force on the object. It is the lack of a centripetal force that causes the driver to conclude incorrectly that an outward force acted on the object.