To predict the period of a semi-circle and isosceles triangle with some moment of inertia after first calculating the moment of inertia of the semi-circle and isosceles triangle about a certain axis.
To do this, we cut out the two shapes from a foam board, measured their dimensions, calculated the moment of inertia for each shape, and predicted a value for the period. After predicting a value for the period, we measured the period experimentally by using a photogate sensor with the oscillation at relatively small angles.
APPARATUS:
Equipment:
Photogate sensor
foam board
method of cutting the foam board
method of measuring the foam cut-out
EXPERIMENT:
- We began by measuring the dimensions of our two shapes
Semi-circle: R = 0.0765-m
Isosceles Triangle: B=0.12-m, H=0.15-m - We began by calculating four moments of inertia.
To calculate the moment for the semi-circle, we first had to calculate the center of mass of the semi circle.
We only needed to find the vertical center of mass for the semicircle, and by symmetry, the horizontal center of mass is exactly half the diameter.
After finding the center of mass we calculated the moment for the semi-circle and the triangle.
From the relationship we found when calculating the center of mass:
For the Triangle: - We then calculated the period of oscillation for each shape.
For the semi-circle:
For the triangle: - After predicting values for the period of each shape with their given orientation, we measured the period with a photogate sensor.
The actual period for a semi-circle with its axis of rotation about the diameter: T=0.5994-s.
The actual period for a semi-circle with its axis of rotation about the outer radius: T=0.5991-s.
The actual period for an isosceles triangle with its axis of rotation about the base: T=0.6091-s
The actual period for an isosceles triangle with its axis of rotation about the apex: T=0.6964-s.
CONCLUSION:
I can't see any of the documents or pictures you attached except for the first one.
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