Performing the simulation: Suspend the pendulum … The average value of k G over the different measured periods T is taken, and the moment of inertia of the bar about a perpendicular axis through its centre of mass is calculated using the equation I G =Mk G 2. F= ma= mgsin (2) The radius of gyration, \(k\), is one half the distance along the x-axis from the point where the slope of the left curve is zero to the point where the slope of the right curve is zero. This so-called reversibility is one of the unique properties of the compound pendulum and one that has been made the basis of a very precise method of measuring g (Kater’s reversible pendulum). 1 Measurement of acceleration due to gravity (g) by a compound pendulum Aim: (i) To determine the acceleration due to gravity (g) by means of a compound pendulum. A special reversible compound pendulum called Kater’s pendulum is designed to measure the value of g, the acceleration of gravity. The period T for a simple pendulum does not depend on the mass or the initial angular displacement, but depends only on the length L of the string and the value of the gravitational field strength g…
constant g. The value of gravity in Salt Lake City (elev.1320 m) according to this model is: 9.81792 m=s2[3][4][5].
1: Free body diagram of simple pendulum motion[2]. 1 Measurement of acceleration due to gravity (g) by a compound pendulum Aim: (i) To determine the acceleration due to gravity (g) by means of a compound pendulum. B5-1: Determining \(g\) Using a Compound Pendulum (ii) To determine radius of gyration about an axis through the center of gravity for the (ii) To determine radius of gyration about an axis through the center of gravity for the Use this value of \(k\) and the mass of the stick to determine the moment of inertia of the stick. The simple pendulum provides a way to repeatedly measure the value of g. The equation of motion from the free body diagram in Figure 1[2]: FIG.
Thus, by measuring the period of a pendulum as well as its length, we can determine the value of \(g\) : \[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\] We assumed that the frequency and period of the pendulum depend on the length of the pendulum string, rather than the angle from which it was dropped. It can be shown that the distance between S and O is equal to l, the length of the equivalent simple pendulum.
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