• 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. Case Analysis: Forecasting Food and Beverage Sales

    113.73% 2 January 263 2190 182.5 182 144.51% February 238 2199 183.25 182.88 130.14% March 247 2211 184.25 183.75 134.42% April 193 2211 184.25 184.25 104.75% May 193 2226 185.5 184.88 104.39% June 149 2250 187.5 186.5 79.89% July 157 2269 189.08 188.29 83.38% August 161 2286 190.5 189.79 84.83%

  2. 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.

  1. The History of the Cubic Equation

    Far from being embraced, complex numbers were initially greeted with suspicion, confusion and even hostility. Cardano's Ars Magna (1545) is traditionally taken to be the birth certificate of complex numbers.

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

    snork, n. snork, v. snorkel, schnorkel snorkle snorl, v. snort, n.1 snort, n.2 snort, v.1 snort v.2 snorter1 snorter2 snorter3 snorter4 snorting, vbl. n.1 snorting, vbl. n.2 snorting, ppl. a. snortle, v. snorty, a. and adv. snory, a. snot, n. snot, v. snoter, a. snotter, n.1 snotter, n.2 snotter, v. snottery snottily, adv. snottiness snottinger snottish, a. snotty, n.

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

    1.2 Simulation The Breve simulation environment was used to implement path finding techniques [5]. Breve is a free, open-source software package which makes it easy to build 3D simulations of decentralized systems and artificial life organisms. Time complexity analysis of the different search algorithms to find optimal paths was performed

  2. Pythagoras’ Theorem.

    Whether someone from the school or Pythagoras himself found the proof can't truly known. Hence the philosophy of Pythagoras is known through the work of his disciples. The school did make several contributions to mathematics. Pythagoras believed that all relations were based on number relations.

  1. This experiment is to measure and calculate the partial molar volumes of sodium chloride ...

    The apparent density is defined as the density of the powder particles themselves and is determined using the equation: ?A=Ms Vs (Equation 9).

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

    put forward and developed but as the case is with most, with each new innovation comes a whole new set of barriers. "Encryption is the conversion of data into a form, called a cipher text, that cannot be easily understood by unauthorized people (searchsecurity.com (c)

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