- Level: University Degree
- Subject: Mathematical and Computer Sciences
- Word count: 962
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.
Extracts from this document...
Introduction
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.
Middle
=
For the connecting rod,
When using the trifilar suspension,
Let m = ( M + Mo )
Then, m = (1848.52 + 1954.8 ) x 10-3 kg
= 3.8033 kg
Error in m is,
= 1.0001 x 10-6 kg
From equation 1,
Let
Error in,
= kgm2
=
=
Error in I ,
kgm2
=
Compound pendulum method for con-rod.
When l = 236 mm,
Error in I ,
=
=
Let Y=,
=
=
Conclusion
M - mass of body,
G - acceleration due to gravity.
Raw data,
L | 1.705 m |
r | 0.0775 m |
Mo | 1.125 kg |
For the oscillations of the trifilar suspension,
T1 | 1.935 s |
T2 | 1.920 s |
T3 | 1.934 s |
Average - T | 1.930 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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