Determination of moment of inertia of a uniform rectangular bar and a connecting rod using the trifilar suspension, and by swinging the connecting rod as a compound pendulum.
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The Trifilar Suspension Tutor : Dr. Yan Name : Manilka Abeysuriya Course : Aeronautical Engineering Group : A - 1 Date : 27 / 01 / 2003 Title : Determination of moment of inertia of a uniform rectangular bar and a connecting rod using the trifilar suspension, and by swinging the connecting rod as a compound pendulum. Introduction : Moment of Inertia can be described as a measure of "unwillingness to change the current motion" of a certain body of mass. In the experiment, the main objective is to find the moment of inertia of a uniform body and an irregular shaped body. Toward achieving this First the center of mass of the bar and the connecting rod was found by balancing them on a knife-edge. Then the bar was placed on the trifilar suspension which is a circular platform suspended by three equally spaced wires of equal length, such that the center of mass of the rod is over the center of the circular platform. Then the whole system is given a small angular displacement, and the periodic time for the oscillations is determined by measuring the time taken for 20 oscillations.
I = For the connecting rod (2nd suspension) I = Discussion : The equation 1 is accurate only for oscillations with small angular displacements. If this displacement is considerably large an error could occur in the final results due to this reason. And also when using the trifilar suspension the center of mass of the object under consideration should be right over the platform. Other wise a additional moment of inertia of the system will cause a increase of the result, actually expected. When measuring the time an error is always possible in the measurement due to differences in human reaction time. Analysis of Error, When I = 0 and M = 0, From equation 1, Error in , = = 7.62 x10-3 = 7.62 x10-3 x = For the uniform rod, Let m = ( M + Mo ) Then, m = (1125 + 1954.8 ) x 10-3 kg = 3.080 kg Error in m is, = 1.01 x 10-6 kg From equation 1, Let Error in, = kgm2 = 5.1 x10-5 x = Error in I , kgm2 = For the theoretical calculation of I for the uniform rod, From equation 2, Let p = I2 + w2 = (0.25452 +.0385 2)
s From Equation 1, Dimensions for uniform rod, Length 254.5mm Width 38.5mm Mass 1954.8g For the oscillations of the system rod and the trifilar suspension, T1 2.056 s T2 2.050 s T3 2.066 s Average - T 2.057 s From Equation 1, Theoretically, Equation 2 For the connecting rod, Mass 1848.52 g T1 2.918 s T2 2.923 s T3 2.922 s Average - T 2.921 s Using Equation 1 for the system of trifilar suspension and the connecting rod, When the connecting rod was suspended by a end let to swing the moment of inertia of the rod about the axis through the point of suspension is given by, ................ Equation 3 Where, T - periodic time M - mass G - acceleration due to gravity l - distance from the point of suspension. Using the parallel axes theorem, Iy1y1 = Iyy + Md2 Iyy = Iy1y1 - Md2.............Equation 4 When l = 236 mm, T1 0.9980 s T2 1.084 s T3 1.072 s Average - T 1.051 s From equation 3, From Equation 4, When l = 100 mm, T1 0.9950 s T2 1.030 s T3 1.040 s Average - T 1.022 s From equation 3, From Equation 4,
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