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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.

Extracts from this document...

Introduction

### The Trifilar Suspension

Tutor        :        Dr. Yan

## 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

kgm2

=

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,

This student written piece of work is one of many that can be found in our University Degree Mathematics section.

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