Trifilar Suspension
Trifilar Suspension
Summary
The polar moment of inertia for an assembly of solid objects was calculated using the trifilar suspension apparatus. The periodic time for the experimental and theoretical results were analysed and compared in order to study the relationship between the mass moment of inertia and the mass of an assembly.
Table of Contents
1. Introduction – page 3 2. Theory – page 4 - 7 3. Apparatus – page 8 4. Procedure – page 9 5. Results – page 10 - 11 6. Discussion – page 12 - 13 7. Conclusion – page 14 8. References – page 14
Introduction
The moment of inertia I is a measure of the resistance of a body to angular acceleration [1]. An important factor as the resulting moment governs the analysis of rotational dynamics with an equation of the form M=I∝ which defines a relationship between several properties including angular acceleration and torque [2]. The polar moment of inertia is the measure of a body’s resistance to torsion and is used to calculate the angular displacement and periodic time of the body under simple harmonic motion [3].
The moment of inertia of any mechanical component that will encounter rotational motion must be analysed as part of the design phase. From the complex assembly of a steam turbine to the simplicity of a flywheel, the periodic time for a component can be compared with other prototypes in order to find the most efficient assembly before going into production.
The trifilar suspension is an assembly that is used to determine the moment of inertia of a body about an axis passing through the body’s mass centre, perpendicular to the plane of motion [4]. Loading the assembly with various objects and with an understanding of the parallel axis theorem, it is possible to determine the total moment of inertia for the entire assembly.
Theory
The moment of inertia of a solid object is obtained by integrating the second moment of mass about a particular axis. The general formula for inertia is:
Summary
The polar moment of inertia for an assembly of solid objects was calculated using the trifilar suspension apparatus. The periodic time for the experimental and theoretical results were analysed and compared in order to study the relationship between the mass moment of inertia and the mass of an assembly.
Table of Contents
1. Introduction – page 3 2. Theory – page 4 - 7 3. Apparatus – page 8 4. Procedure – page 9 5. Results – page 10 - 11 6. Discussion – page 12 - 13 7. Conclusion – page 14 8. References – page 14
Introduction
The moment of inertia I is a measure of the resistance of a body to angular acceleration [1]. An important factor as the resulting moment governs the analysis of rotational dynamics with an equation of the form M=I∝ which defines a relationship between several properties including angular acceleration and torque [2]. The polar moment of inertia is the measure of a body’s resistance to torsion and is used to calculate the angular displacement and periodic time of the body under simple harmonic motion [3].
The moment of inertia of any mechanical component that will encounter rotational motion must be analysed as part of the design phase. From the complex assembly of a steam turbine to the simplicity of a flywheel, the periodic time for a component can be compared with other prototypes in order to find the most efficient assembly before going into production.
The trifilar suspension is an assembly that is used to determine the moment of inertia of a body about an axis passing through the body’s mass centre, perpendicular to the plane of motion [4]. Loading the assembly with various objects and with an understanding of the parallel axis theorem, it is possible to determine the total moment of inertia for the entire assembly.
Theory
The moment of inertia of a solid object is obtained by integrating the second moment of mass about a particular axis. The general formula for inertia is:
References: [1] R.C. Hibbeler “Engineering Mechanics – Dynamics” Tenth Edition p377 [2] http://en.wikipedia.org/wiki/Moment_of_inertia [3] http://en.wikipedia.org/wiki/Polar_moment_of_inertia [4] R.C. Hibbeler “Engineering Mechanics – Dynamics” Tenth Edition p378 [5] R.C. Hibbeler “Engineering Mechanics – Dynamics” Tenth Edition p378 Trifilar Suspension Dynamics Laboratory sheet