PHY 122 Rotational motion lab report - PHY 122 Rotational...

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Unformatted text preview: PHY 122: Rotational Motion Kyle Kas Branson, Tyler Friday 10:00AM-11:50AM TA: Ankush Objective Section: The objective of this lab was to understand angular acceleration, torque, and moment of inertia for a system of a mass hanging from a pulley. Experimental Data: Mass of Block = 0.4432 kg Mass of hanging weight = 0.020 kg Dimensions of block = 0.050 m x 0.040 m x 0.030 m Radius of Small Pulley = 0.0048 m Radius of Medium Pulley = 0.0143 m Short axis Small pulley Medium pulley Angular acceleration Initial angular position Initial angular velocity Final angular position Final angular velocity Long axis Small pulley Medium pulley 6.69 rad/s2 17.4 rad/s2 10.8 rad/s2 27.6 rad/s2 0 0 0 0 0 0 0 0 140.848 rad 55.519 rad 153.764 rad 52.587 rad 42.76 rad/s 42.76 rad/s 55.5 rad/s 53.06 rad/s Data Analysis Section: Static moment of inertia 1 ( + ) 12 For the short axis: = (0.4432 )((0.050 = 1.514 ∗ 10 For the long axis: = (0.4432 )((0.040 = 9.233 ∗ 10 Error for static moment of inertia = ∆ = ∗∆ + ∗∆ + ) + (0.040 ) ) ) + (0.030 ) ) ∗∆ ∆ = ( 12 + 12 )∗∆ + ( 6 )∗∆ + ( 6 )∗∆ For the short axis: ∆ = ( (0.050 ) (0.040 ) + ) ∗ (0.00001 12 12 ) + ( (0.4432 )(0.050 6 ) ) ∗ (0.00005 ) + ( ) ∗ (0.00005 ) + ( (0.4432 )(0.040 6 ) (0.4432 )(0.030 6 ) ) ∗ (0.00005 ) ) ∗ (0.00005 ) ∆ = 2.4 ∗ 10 For the long axis: ∆ = ( (0.040 ) (0.030 ) + ) ∗ (0.00001 12 12 ) + ( ∆ (0.4432 )(0.040 6 ) = 1.8 ∗ 10 Dynamic moment of inertia − = For short axis and small pulley = (0.020 = (0.020 = (0.020 = (0.020 )(0.0048 ) 9.8 − (0.0048 )(6.69 ) )(17.4 ) )(10.8 ) )(27.6 ) 6.69 For short axis and medium pulley )(0.0143 ) 9.8 − (0.0143 17.4 For long axis and small pulley )(0.0048 ) 9.8 − (0.0048 10.8 For long axis and medium pulley )(0.0143 ) 9.8 − (0.0143 27.6 Error in dynamic moment of inertia ∆ ∆ = = ( ( For short axis and small pulley ∗∆ − )) ∗ ∆ = 1.4017 ∗ 10 = 1.5699 ∗ 10 = 8.6650 ∗ 10 = 9.7561 ∗ 10 ∆ = ((0.0048 9.8 − (0.0048 ) ) 6.69 ) ∗ (0.00001 6.69 ) = 7.0 ∗ 10 For short axis and medium pulley ∆ = (0.0143 ) 9.8 − (0.0143 )(17.4 ) 17.4 ∗ 0.00001 = 7.8 ∗ 10 ∗ 0.00001 = 4.3 ∗ 10 ∗ 0.00001 = 4.9 ∗ 10 For long axis and small pulley ∆ = (0.0048 ) 9.8 − (0.0048 )(10.8 ) 10.8 For long axis and medium pulley ∆ = (0.0143 ) 9.8 − (0.0143 )(27.6 ) 27.6 Results Section: Static moment of inertia: Short axis Long axis (1.514 0.002)*10-4 kg m2 (9.23 0.02)*10-5 kg m2 Dynamic moment of inertia: Short axis small pulley Short axis medium pulley Long axis small pulley Long axis medium (1.4017 0.0007)*10-4 kg m2 (1.5699 0.0008)*10-4 kg m2 (8.665 0.004)*10-5 kg m2 (9.756 0.005)*10-5 kg m2 = −2.424 ∗ 10 Discussion and Conclusion Section: The objective of this lab was to understand angular acceleration, torque, and moment of inertia for a system of a mass hanging from a pulley. The concepts studied in this lab are angular acceleration, moment of inertia and torque. Angular acceleration is the rate of change of angular velocity and is usually measured in rad/s2. Moment of inertia is a body’s tendency to resist angular acceleration. Torque is the likeliness that a force will cause an object to rotate. At the beginning of the lab the metal block’s dimensions and mass were measured. Then the block was put on the rotary through its short axis, and the mass was wound up on the medium pulley. Then the mass was let go with the sensors recording data to the program. Then this process was repeated but with the mass wound around the smaller pulley. Then the block was placed on the rotary through the long axis and the process was repeated. The results came out quite well. The calculated static moment of inertia and the dynamic moment of inertia were very close to each other. Also the torque value was close to what was expected. Some possible sources of error could be setting up the equipment wrong. Another possible source is not using the program right to acquire data. Error could also happen in calculations. The data we received in the lab was good and what was expected. The dynamic and static moments of inertia were very close to each other. Therefore, the objective of this experiment has been accomplished with victory! ...
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