Lab #8 - Moment of Inertia Name Katie Ellis Group Names Felicia Eden Purpose The group compared the experimentally measured and calculated moment of

Lab #8 - Moment of Inertia Name Katie Ellis Group Names...

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Moment of Inertia Name: Katie Ellis Group Names: Felicia, Eden Purpose: The group compared the experimentally measured and calculated moment of inertia of multiple objects to the given integrated moment of inertia formulas for each specific shape. We found that the calculated moment of inertia, based off the conservation of energy, came acceptably close to the value calculated from the integrated formula from I = r 2 dm . Procedure: To find the moment of inertia, without actually using the definition, the group created a system in which energy was conserved. This means that only conservative forces were allowed to act on the experimental system, which can only include gravity and/or a spring force. When energy is conserved then Δ PE = Δ KE and therefore mg Δ y = 1 / 2 ( I ω 2 )+ 1 / 2 ( m v 2 ) . By algebraically arranging the equation to solve for I we could calculate the moment of inertia using the conservation of energy where r / v ¿ 2 ∗( 2 mg Δ y m v 2 ) I = ¿ . Using the moment of inertia apparatus as shown in the figures to the right, the group found the velocity and change in position for the platform, a hoop, a disk and a rod with the help of a labquest photogate mounted on the pulley. By hanging a mass of the end of the pulley, the platform could rotate whatever object that it held, creating the necessary rotational motion and linear motion to calculate the moment of inertia. These values were then used to calculated the moment of inertia for each object in order to directly compare them to the integrated version. Data: Through four trials the group measured the velocity and mass required to rotate the moment of inertia apparatus with each specific object attached. The apparatus had a radius of 2.20cm and the constant acceleration due to gravity was 9.8 m/s 2 . Both of these values were constant throughout each trial and used in the calculation of the moment inertia as such. Object Mass Hung from Pulley (g) Mass of Object (kg) Velocity (m/s) Position (m) Moment of Inertia (kg*m 2 ) Integrated Moment of Inertia (kg*m 2 ) Platform 50 - 0.216 0.210 0.00211 - Disk 300 4.82 0.123 0.195 0.0344 0.0377 Hoop 300 4.25 0.114 0.255 0.0536 0.0655
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Rod 100 0.8295 0.034 0.120 0.0963 0.100 Each object was rotated about an axis vertically inserted through the center of mass. The only exception to this was the rod in which we used the parallel axis theorem in order to compare the two moment of inertia values. The mass hung from the pulley and string was the mass used in the calculation of the moment of inertia since it was the mass needed to start rotational motion and therefore convert the potential energy of the system into kinetic energy. Masses of the objects were used in the integrated moment of inertia equations as they represented the actual amount of mass the object held, not the mass needed to start motion. When calculating
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  • Spring '15
  • Farris

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