Centrifugal motion at a fun fair
Teaching Guidance
for 14-16
Consider using this thought experiment
about a common example of circular motion to stimulate a fruitful classroom discussion.
Suppose that two boys, A and B, visit one of those amusements at a fair in which people sit on a floor that rotates. A and B enter the room while the floor is at rest, and sit on the polished floor. Knowing the trick of the performance, A glues himself to the floor. When the floor begins to spin A notes that a mysterious force seems to pull him outward. But for the glue, it would make him slide out to the wall.
B, without glue; slides out to the wall if A does not hold on to him, exerting an inward pull on him. Each boy feels he is struggling against centrifugal force
.
But now let a stationary observer take a bird's eye view from above. Seen from outside the spinning room, A and B are each moving in a circular orbit; and each needs a real inward force to keep him in orbit. For B, the force is the inward pull which A provides: for A it is the pull of the sticky floor on him. The boy A merely imagines an outward force on B because he has to apply a real inward force to him. As the outsider sees, these inward forces are not neutralizing a mysterious outward force; they are making an inward acceleration; they are making A and B move in a curve.
The outside observer offers a further comment. He sees that when A lets go; B continues along a tangent (if there is no friction). B's successive positions along that tangent are farther and farther out from the centre of the circle; so, as seen by A (revolving with the floor), B seems to be sliding out along a radius. But really B is just continuing a straight (tangent) path, a simple example of Newton's first law.
Centrifugal force is a delusion due to living in the rotating system and trying to forget it.
The rotating-floor discussion leads straight to this view. To people sitting on the floor in a concealing fog – and ignoring its motion – there is an outward field of force, endowing every mass m with an outward force mv 2R.
Unless some real agent applies an inward force to balance this, any object left alone will seem to slide outward with acceleration v 2R. A sober view from outside says that both the outward field of force and the outward sliding are delusions due to living in a rotating framework and not allowing for its motion.
