Theory: Using the formula of Torque= Inertia*Angular acceleration, I can "rework" the expression into Angular acceleration= - angular frequency^2*Theta, and assuming theta is very small, I can find the period (T) as the period is just 2*pi/angular frequency.
Procedure: Cut out a semicircle "disk," measure its mass and radius, set it up to act as a pendulum once as swinging from the "flat bottom" and once from the curve. Give it a slight nudge to begin oscillating, and have the computer measure the period for each oscillation (add thin stripe of tape to the semi circle disk so it quickly breaks the "beam counter" of the computer for each oscillation of the pendulum, record actual result and compare with calculated result.
Apparatus
Period Results
*From the Curve
*Period 0.600427 seconds
*From the "flat bottom"
*Period 0.604880 seconds
Dimensions of Semi circle
*This will be needed to determine the distance from the pivot as the semi circle acts as a pendulum
*Plugging in the Radius we get 0.003289202 meters from the bottom.
*So the distance between the pivot, when its at the flat bottom, is the same as the center of mass (d_1 = 0.003289202)
*And the distance between the pivot and the center of mass when the semi circle is pivoted at the curve is the Radius minus the distance of the center of mass (d_2=0.0044607980
Calculations of moment of Inertia of Semi-Circle
Calculation to determine period (From the flat bottom)
*Period from flat bottom: 0.14571 s, difference from actual 75.9%
*Period from the curve: 0.161102 s, difference from actual 73.2%
Conclusion
*Because of the amount of error I received, I do not consider this a very good experiment for confirming the period from an unusual pendulum.
Error Analysis
*Because we had to create our own semi-circle pendulums, I do not know if my semi-circle pendulum was ideal. It was traced from a protractor and cut into shape, so "grooves" and dimensions of the semi-circle may have invalidated my assumption from my calculations that I was working with an actual semi-circle.
*Theta needs to be extremely small for my calculations to reflect reality, since the actual periods were so much larger than my calculated amount, I believe theta was far too large during the experiment. Perhaps I added to much force to begin the oscillations.
*Measurements were all done with a ruler for the Semi-circle, causing uncertainty in measurements.
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