 # Abstract

Abstract:

The aim of a trifilar experiment is to evaluate the moment of inertia of a cylindrical/circular plate using apparatus set up in the trifilar suspension, then to compare it to theoretical results in order to judge accuracy, to then investigate how various objects placed in different locations on the system affect the period of oscillation of the plate.

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Theory:
To obtain the moment of inertia of a solid object you must integrate the second moment of mass about an axis. The formula most likely used for inertia is Ig=mk2

Ig being Inertia in Kgm2 about the centre of mass, m being the Mass in Kg, k being the radius of gyration about mass centre in m. To calculate the inertia of an assembly, Ig must be by mh2 (local mass in Kgh-being the distance between the parrallel axis which goes through the local mass centre and the mass centre for the full system. The Parralllell axis theory must be put to use to each member of the system, therefor I= (Ig+mh2)

In this experiment an array of three solid objects are placed on the platform, which is hung from three chains in order to create a trifilar suspension. The periodic time for small oscillations about a vertical axis is related to the Moment of Inertia

Procedure

The Trifilar suspension was set up and the length of tha chains were measured with a measuring tape coming in at two metres long each. In order to have multiple takes on the experiment while maintaining the same force, a tangential reference line should be created using a marker pen or pencil onto the circular platform and mark another point of reference on the table

Results and discussion

Objects placed on the circular platform and their respective Inertia are as follows;

Cylindrical solid
I=mr^2/2=11.65×10^-3 kg.m^2

Cylindrical tube
I=m/2(ro^2+ri^2)=2.898×10^-5 kg.m^2

Square hollow
I=m/6(ao^2+ai^2)=6.939×10^-3kg.m^2

Circular platform
I=(mr^2)/2 =0.1215 kg.m^2

Therefore;

Total Inertia
Itot = 0.14299 kg.m^2#

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