You can still buy a centrifugal railway, although it will not be as elegant as the one below from Miami University. Today, to avoid the forbidden word centrifugal, we use names like "loop-the-loop". The 1916 Knott catalogue description of a similar piece of apparatus is illuminating: "Centrifugal Railway, illustrating the opposition offered by a moving body to any influence exerted to counteract its tendency to move in a straight line. This apparatus consists of a looped circular railway down which a body may roll unobstructed. At one point in the loop illustrated, the body is held by centrifugal force against the underside of the track in opposition to the force of gravity." This description suggests the bogus idea of equilibrium so beloved of introductory students, and misses the point that if the starting point is chosen properly, the body will actually be in momentary free fall at the highest point of the loop.
This example was made by James W. Queen of Philadelphia, and is described in the 1881 as being "four feet long, of neatly japanned tin, on a wooden base with leveling screws and glass ball .. $8.00 ."
The centrifugal railway below is at the University of Texas at Austin, and was also made by Queen. It has been used constantly for demonstrations and over the years it has been reworked, with the rails being replaced by brass strips.
The tin-plate railway below is not a true centrifgal railway, but does show that the speed of the marble increases in the valleys and decreases at the peaks. It probably started its life as a child's toy ca. 1900, and is now in the collection at the University of Cincinnati.
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