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physics lab 8-rotational motion 79 out of 85

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PHY 122

Lab 8: Rotational Motion T.A: Monday at 2:00 p.m Abstract: This experiment was done in order to determine whether the moment of inertia depends on the axis of rotation or not and to determine if energy is conserved in rotational motion. A block was placed on a rotary encoder and a string attached to that was wrapped around a pulley and Data Analysis was used to record the angular speed versus time of the block. The results show that both the static and dynamic moments of inertia depend on the axis of rotation of the block (as the values of the total static inertia 1.489∗10 −4 2∗10−7 m2 on the short axis was +/- kg* and on the long axis was −5 −7 2 −4 9.09∗10 +/- 1∗10 kg* m . The dynamic moment of inertia was 1.1483∗10 −7 2 −4 −7 2 +/- 4∗10 kg* m , 1.2273∗10 +/- 4∗10 kg* m on the small and −5 −7 medium pulleys respectively and on the long axis ( 8.7464∗10 +/- 9∗10 kg* m2 9.0599∗10 −5 3∗10 −7 m 2 , +/- kg* for the small and medium pulleys respectively.) The results also indicate that regardless of the size of the pulley the dynamic moment of inertias matched up with the static moment of inertias. As the total amount of energy lost in the system was low (-.0034 J ), it was determined that energy was conserved in the rotational motion with a slight loss of energy over time due to friction. The average torque from friction was also found to be -.0027 N*m. The results found in this lab coincided with what was expected as the energy was conserved and the inertia depended on the axis of rotation. The torque also gave a reasonable answer as it acts in the opposite direction of gravity and was anticipated to have the opposite sign, which it does. Objective: The objective of this lab experiment is to verify the moment of inertia using geometric and dynamic methods for a rectangular prism. Conservation of energy was also tested for rotational motion of the rectangular prism. Equipment: The equipment used in this lab was a steel block fixed on a rotary encoder attached to a string which was either wound on a small pulley or a medium pulley and Data Analysis was used to record the angular speed and time of the rotation. Procedure: The length, width and height of the steel block were first measured. The block was then weighed. The block was first mounted on the rotary encoder through its shortest axis. The string was wound clockwise around the small pulley. Data analysis was started and the string was then released. Data Analysis recorded the rotational speed and the time. This same procedure was repeated for the medium pulley. The block was then removed from the rotary encoder and was remounted through its long axis. The trial winding the string and releasing it was repeated for the small and medium pulley as well. Results: −4 −7 I❑ s shortaxis.489∗10 +/- 2∗10 kg* m 2 I❑ slong axis9.09∗10 −5 1∗10 −7 +/- kg* m 2 I❑ d shortaxis,small pulley.1483∗10 −4 4∗10 −7 +/- kg* 2 m I❑ d shortaxis,medium pulley2273∗10 −4 4∗10 −7 +/- kg* m 2 I❑ −5 −7 d longaxis,small pulley8.7464∗10 +/- 9∗10 kg* m 2 −5 −7 I❑ d longaxis,mediumpulley9.0599∗10 +/- 3∗10 kg* 2 m ∆ K .0764 J ∆U -.0798 J ∆ E -.0034 J τ -.0027 N*m Discussion The theories proved in this lab were that inertia depends on the axis of which the object rotates and that energy was conserved for rotational motion. In this lab, a constant torque was applied to a rectangular prism, giving it an angular acceleration about its center of mass. The static moment of inertia was found for the block on the short
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