• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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.

...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.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related University Degree Mathematics essays

  1. The trifilar suspension is used to determine the moments of inertia of a body ...

    0.013 kg/m Inertia of rod (Hanging method) 0.042 kg/m Discussion In this experiment two different sets of readings where gathered and recorded. Both the bar and the rod where tested by the trifilar method. However the rod was placed under one more test, the knife edge, results for these experiments can be seen on table one.

  2. Case Analysis: Forecasting Food and Beverage Sales

    Hence, to understand and measure these components, the forecast procedure involves initially removing the component effects from the data (decomposition). After the effects are measured, making a forecast involves putting back the components on forecast estimates (recomposition). Pursuing this can help Karen take a proper judgment.

  1. Pythagoras’ Theorem.

    It allows us to find the third side of a right-angled triangle given the other two sides. The formal definition is 'the square of the hypotenuse of a right angle triangle is equal to the sum of the square of the other two sides'.

  2. OPTIMAL PATH PLANNING USING AN IMPROVED A* ALGORITHM FOR HOMELAND SECURITY APPLICATIONS

    using a timer function in the Steve language, which is part of Breve. Time complexity analysis of the various search algorithms showed the efficiency of the different algorithms. Space complexity analysis of the search algorithms was also performed. Space complexity analysis showed not only the efficiency of the different algorithms but also shows why a particular algorithm fails.

  1. This paper intends to examine the words starting with given in the Oxford ...

    v.3 snigger, n.1 snigger, n.2 snigger, v.1 snigger, v.2 sniggerer sniggering, vbl. n. sniggering, ppl. a. 'Sniggers, int. snigger snee sniggery, a. snigging, vbl. n.1 snigging, vbl. n.2 sniggle, n.1 sniggle, n.2 sniggle, n.3 sniggle, v.1 sniggle, v.2 sniggle, v.3 sniggler1 sniggler2 sniggler3 sniggling, vbl.

  2. Investigating the affect that Body Mass Index and Waist-to-hip Ratio has on the Perception ...

    The overall conclusion was that over the last three decades a significant change in the idealized female body shape has occurred. However, later studies showed that Morris et al results were inaccurate and that when the actual WHRs were computed they remained within a feminine 0.68-0.72 range thus, clearly showing

  1. History and Social Context of Mathematics.

    are erroneous. Some sections within the Sulbasutras which give rules for the construction of right angles using lengths of cord divided into Pythagorean Triples. It is disappointing, however, that all of these triples were known during the Mesopotamian times between 2000 and 600 BC and may have percolated South or have passed across to the Vedic people from Mesopotamia.

  2. Logistics equation. This coursework relates to an investigation and description of the systems ...

    The next group of graphs reach chaos, as they never converge to steady states. There is no set pattern and the numbers randomly change although, every now and again it begins to look like the values are converging into a pattern when suddenly they can break down into a chaotically random state again.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work