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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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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.

...read more.

Middle

 kgm2

                           =image49.png

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,     image26.pngimage05.png

image51.pngimage27.png

                                       =  1.0001 x 10-6 kg

From equation 1,
        
image29.png

Let                              image30.pngimage31.png

 Error inimage30.png,              image33.png

image52.png

                                                                                                 = image54.png kgm2

image36.png= image54.pngimage55.png

                                        =        image56.png

Error in I  ,image05.pngimage05.png

image39.png

image57.png kgm2

                                     = image56.png

Compound pendulum method for con-rod.

When l = 236 mm,

Error in I ,

image59.png

image60.png

image61.png =   image62.png

        =   image63.png

Let Y=image64.png,    image65.png

image66.png

image67.png        =        image68.png

        =  image70.png

...read more.

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,

image84.png

image85.png

image86.png

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,

image87.png

image88.png

image89.png

Theoretically,

image05.pngimage06.png        Equation 2

image07.png

image08.png

image09.png

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,

image10.pngimage11.png

image12.png

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,

image13.png……………. 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

image01.png

When l = 236 mm,

T1

0.9980 s

T2

1.084 s

T3

1.072 s

Average - T

1.051 s

From equation 3,

image14.png

image16.png

image17.png

From Equation 4,

image18.png

image19.png

When l = 100 mm,

T1

0.9950 s

T2

1.030 s

T3

1.040 s

Average - T

1.022 s

From equation 3,

image20.png

image21.png

image22.png

From Equation 4,

image23.png

image24.png

...read more.

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