B6 Kater's Reversible Pendulum

# B6 Kater's Reversible Pendulum - EXPERIMENT Katers...

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EXPERIMENT Kater’s Reversible Pendulum Introduction: One of the most important physical constants is g , the acceleration due to gravity. It provides a secondary definition for the unit of force in mechanics and is therefore very important for all dynamical measurements. The value of g can be measured directly with a well- conducted experiment on a free-fall apparatus or on a good air track to a reasonable accuracy (about 1%). To improve the accuracy, other methods must be used. The use of a pendulum is attractive because the only quantities needed to calculate g are its dimensions and its period of oscillation. For very accurate measurements, the limiting feature turns out to be the precision with which the centre of mass and the moment of inertia of the pendulum can be determined. In 1817 Kater, following a suggestion of Bessel, developed a reversible physical pendulum that made possible the accurate measurement of the local acceleration due to gravity g . High accuracy is achieved because there is no longer a need to determine the moment of inertia of such a reversible physical pendulum. By definition, a reversible pendulum is one which can be swung from either of two stable pivot points. When the mass distribution of the pendulum is adjusted so that the periods are the same from either pivot, then this period is the same as a simple pendulum having a length equal to the distance between the pivots. While this may seem to be a simple property, it has great power in determining the value of g to high accuracy. The beauty of Kater’s invention is that the only geometrical quantity needed is the distance between the pivots. The position of the centre of mass and the moment of inertia are not required. Using pendulums of this type, the National Bureau of Standards determined the value of g to be in Washington in 1936. Similar precise measurements were made by government standards laboratories at Teddington in England and at Potsdam in Germany at about the same time. During a typical three-hour laboratory session in this physics course, a student should be able to measure g to an accuracy of 2 / 003 . 0 080 . 980 s cm ± % 1 ± . Theory: The mechanical design of the pendulum is not important to the derivation of the theory; it is only necessary that the pendulum can be swung from the two pivot points. Our form of Kater’s pendulum consists of a long bar with two knife edges placed near the ends. Attached to the bar are two bobs, or circular weights. One of these is lighter than the other. Provision is made to adjust the position of the bobs on the bar to find the points of equal period. There is no

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## This note was uploaded on 04/01/2011 for the course PHY 135 taught by Professor Wagihghobriel during the Spring '11 term at University of Toronto.

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B6 Kater's Reversible Pendulum - EXPERIMENT Katers...

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