AIM: To determine the moment of inertia of a horizontal rectangular drop bar about its center of mass using the bifilar suspension technique.
The bifilar suspension is a technique used to determine the moment of inertia of any type of object about any point on the object. This is done by suspending two parallel cords of equal length through the object examined. However, the approach taken for this experiment is to determine the moment of inertia of a drop by suspending the cords through the mass centre of bodies, obtaining an angular displacement about the vertical axis through the centre of mass by a sensibly small angle.
SYSTEM LAYOUT AND APPARATUS USED
The apparatus used for this experiment consists of a uniform rectangular drop bar suspended by fine wires (assumed to have negligible weight contribution to the system). This rectangular bar contains holes equidistant from each other and two extra with equal masses of 1.85kg, are made to peg through these holes. Chucks are also in place to alter length of suspended wires.
In addition an enclosed-type measuring tape and weight balance were also used for the experiment.
A diagram on the arrangement of the apparatus used is illustrated below:
- With the bar suspended by the wires, the length L was adjusted to a convenient extent and then distance, b, between the wires was measured.
- The bar was then tilted through a very small angle about the vertical axis and time taken for 20 oscillations of the bar, was recorded. From this, the periodic time was also calculated.
- The length L was further adjusted and the time taken for another 20 oscillations was recorded.
- The inertia of the rectangular bar was then increased by including the “two 1.85kg masses” symmetrically on either side of the centerline distance x apart.
- Then step 3 was repeated but with different values of L
- The length of the wire L was then fixed at a value and the time taken was recorded for 20 oscillations at varying distances x, between the two 1.85kg masses.
- The rectangular bar was then detached from the apparatus arrangement and taken to weight balance in order to determine the mass of the bar.
- The internal diameters of the holes, the thickness of the rectangular were also measured.
- All measurements and data recorded were collated for experimental analysis.