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Where You Taught ”compound Pendulum” In Your Secondary School? by basketbrain(m): 9:02pm On Oct 30, 2014 |
I guess we re all used to simple pendulum; secondary physics. Remember those days, WAEC practicals the pendulum bob, string, calculating the number of oscillation and time taken. Good, but were you taught Compound pendulum? My answer No. Let me know if it was just my physics teacher being lazy. |
Re: Where You Taught ”compound Pendulum” In Your Secondary School? by basketbrain(m): 9:32pm On Oct 30, 2014 |
Compound pendulum The length L of the ideal simple pendulum discussed above is the distance from the pivot point to the center of mass of the bob. Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum. The appropriate equivalent length L for calculating the period of any such pendulum is the distance from the pivot to the center of oscillation.[16] This point is located under the center of mass at a distance from the pivot traditionally called the radius of oscillation, which depends on the mass distribution of the pendulum. If most of the mass is concentrated in a relatively small bob compared to the pendulum length, the center of oscillation is close to the center of mass.[17] The radius of oscillation or equivalent length L of any physical pendulum can be shown to be where I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the center of mass. Substituting this expression in (1) above, the period T of a compound pendulum is given by for sufficiently small oscillations.[18] A rigid uniform rod of length L pivoted about either end has moment of inertia I = (1/3)mL2. The center of mass is located at the center of the rod, so R = L/2. Substituting these values into the above equation gives T = 2π√ 2L/3g . This shows that a rigid rod pendulum has the same period as a simple pendulum of 2/3 its length. Christiaan Huygens proved in 1673 that the pivot point and the center of oscillation are interchangeable.[19] This means if any pendulum is turned upside down and swung from a pivot located at its previous center of oscillation, it will have the same period as before and the new center of oscillation will be at the old pivot point. In 1817 Henry Kater used this idea to produce a type of reversible pendulum, now known as a Kater pendulum, for improved measurements of the acceleration due to gravity. |
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