PHY 121 Roational Motion.pdf

PHY 121 Roational Motion.pdf - PHY 122 Lab Rotational...

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Unformatted text preview: PHY 122: Lab: Rotational Motion Name: Thomas Andrews Group members’ names: Shannon Mendovich, Patrick Champagne, Trevor Baldwin Group number: 1 Class Number: 13726 Day and Time: Monday, 8:00 AM Objective: The objective of this lab is to look at rotational motion from an energy viewpoint. This is done by a constant torque that will create a constant angular acceleration. Another objective will also be top show that the moment of inertia depends on the rotation axis for a given oject. Experimental Data: Mass of block: 0.432kg Mass of hanging mass: 0.02j g rs = 0.0048m rm = 0.0143m Table 1: Short Axis Small Long Axis Long Axis 9.47 rad/s2 27.4 rad/s2 107.88 rad 35.90 rad 43.81 rad/s 41.89 rad/s Short Axis 19.9 rad/s2 17.9 rad 27.4 rad/s Data analysis: Calculations for short axis with small pulley: Static Moment of Inertia: 1 Is = 1—2M(a2 + b2) 1 IS = 1—20.432(0.0492 + 0.042) IS = 1.44 * 10‘4Kgm2 Error Analysis: A, — (“SA )2+(0’slb)2+(a’sl )2 5— 0a a. 6b ' 6m m 2 1 2 1 2 1 _ _ _ 2 2 (IZmZaAa) +(12m2bAb) +(12(a +b )Am) AIS 2 Al — (i (0 432)(2) (0 04-9)(0 00005))2 + (i (0 432) (2) 0 04)(0 00005))2 + (—1-( 04-92 + 042)(0 001)) s — 12 - . . . 12 . ( . . 12 . . . AIS = 4.03 * 10-7 Dynamic Moment of Inertia: g — TC!) 0! 9.8 — ((0.0048)(6.26)) 6.26 Id = 3.2 * 10‘3kgm2 Id=mr( 1d = (0.432)(o.0048)( Error Propagation: 61d Ald = 'a—a‘aa Ala = V ((mgra—2)(Aa))2 AId = J (((0.432)(9.8)(0.0048)(6.26)‘2)(0.017))2 AId = 1.71 * 10—5 Calculations for small pulley with medium Pulley: Static Moment of Inertia: 1 = _ 2 2 IS 12M(a + b ) 1 2 2 Is = EO.4BZ(0.049 + 0.04 ) IS = 1.44 * 10—41(ng Error Analysis: A, — (51s,. )2+(6’sib)2+(a'si )2 5— aa a 6b 6m m 2 2 2 1 1 1 2 2 A15: (-1—2m2aAa) +(fim2bAb) +(fi(a +b )Am) ? 2 AI — (1(0 432)(2) o 049 0 00005 )2 + (i (0 432)(2)(0 04)(0 00005)) + (i( 0492 + 042)(0 001)) 5 _ 12 ' ( ' )( ' ) 12 - . . 12 _ _ . AIS = 4.03 * 10-7 Dynamic Moment of Inertia: g — ra a ) 9.8 — ((0.0143)(19.9) _19.9 ) Id = 2.9 * 10'3kgm2 Id=mr( 1d = (0.432)(0.0143)( Error Propagation: 01d Ald = '6; 6a Nd = a} ((mgra—2)(Aa))2 Nd = 1/(((0.432)(9.8)(0.0143)(19.9)‘2)(0.35))2 Ald = 5.35 * 10‘5 Calculations for Long Axis and Small Pulley: Static Moment of Inertia: 1 Is = 1—2-M(a2 + b2) 1 IS = 1—2-0.432(0.042 + 0.032) Is = 9.0 * 10‘5Kgm2 Error Analysis: A, _ (“SA )2+(015Ab)2+(01si )2 5‘ aa “ 00 am m 1 2 1 2 1 2 = — — _ 2 2 AIS (lZmZaAa) +(12m2bAb) +(12(a +b )Am) 2 2 2 A15 (—11—2'(0.432)(2)(0.04)(0.00005))‘ + (é(0.432)(2)(0.03)(0.0‘0005)) +( —1~—( 042 + 032)(0 001)) 12 . . . AIS = 2.08 * 10'4 Dynamic Moment of Inertia: g — m: a I 9.8 — ((0.0048)(9.47) 9.47 ) Id = 2.1 * 10‘3kgm2 Id=mr( 1d = (0.432)(0.0048)( Error Propagation: Na = 1/ ((mgra‘zXAaDz Ald = J(((0.432)(9.8)(0.0048)(9.47)—2)(0.033))2 Aid = 7.74 * 10—S Calculations for Long Axis Medium Pulley: Static Moment of Inertia: 1 __ 2 2 15—12M(a +b) 1 IS = 130.432(0.042 + 0.032) IS = 9.0 * 10—51(ng Error Analysis: 615 2 615 2 615 2 “s— (ea—a“) WW”) Wham") 1 2 1 2 1 2 = — _ _ 2 2 AIS (lZmZaAa) +(12m2bAb) +(12 (a +b )Am) 2 2 2 1 1 1 A15 (E(0.432)(2)(o.04)(0.00005)) +(E(0.432)(2)(o.03)(o.00005)) +(1—2—(.042 +.032)(o.oo1)) AIS = 2.08 * 10-4 Dynamic Moment of Inertia: g—ra a ) 9.8 — ((0.0143)(27.4) 27.4 ) Id = 2.1 * 10‘3kgm2 Id=mr( I, = (0.432)(0.0143)( Error Propagation: 01d AId = “£66! Nd = x! ((mgra—ZXACZDZ A1,, = w/(((0.432)(9.8)(0.0143)(27.11.)-2)(0.011))2 A1,, = 8.87 * 10—7 Results: Short Axis Long Axis 1.44 * 10—41(ng 9.0 * 10—51(ng i403 * 10‘7 Kng i208 * 10'4 1(ng Long Axis, Long Axis, Small Pulley Medium Pulley 2.1 * 10—3kgm2 i774 * 10'5 Kgm2 i887 * 10'5 1(ng Discussion and Conclusion: Overall, the objective of this lab was to show that the moment of inertia depends on the axis of rotation. Also, to look at rotational motion from an energy point of View. The moment of inertia is defined as the difficulty for an object to rotate. There are two types of moment of inertia, Dynamic and Static. These will be calculated through the following experiments. To test this concept, there were four experiments. All of these experiments changed the pulley and the axis of rotation. The first experiment was a short axis with a small pulley. The second was a medium pulley and a short axis of rotation. The third was a long axis of rotation and a small pulley. The last experiment was a long axis of rotation and a medium pulley. All of these experiments were performed in the same way. The mass was placed on the axis and another mass was wrapped around a pulley. Then, the mass will pull the other mass causing the mass to rotate. That is how the moment of inertia is calculated. At the end, all of the moment of inertia and angular velocities were calculated. The results of this lab showed that the moment of inertia does depend on the axis of rotation. The results for the short axis and small pulley are 3.2 * 10‘3kgm2. This was for the dynamic moment of inertia. The static moment of inertia was 1.44 * 10‘4Kgm2. As the results show, There is a difference between the static and dynamic moment of inertia. This stayed true for the rest of the four experiments. Although there were some errors in the experiments. Some systematical error could be the friction of the pulley and the friction between the pulley and the string. Also, there could be error in the weight of the mass and the weight of the string was not accounted for. There could also be statistical errors. The angular velocity could have statistical error because it was calculated from a line of best fit. This is a statistical error because the line of best fit is not an accurate measurement. Overall, there were some errors in the lab, but the main objectives were achieved. In the end, the theory that the moment of inertia depends on the axis of rotation was confirmed. Rotational Motion.ds 04/10/2017 09:03 AM Graph 1 . r" I I" . I." _ x _l. 01 O 8 o Angular Position( rad ) 01 O O .h 0 O 'ty'grad/s 2))"- o m ( Slope) 9.47 :t 0.033 b ( Y Intercept) -1.52 :t 0.096 r 1.00 Mean Squared Error 0.127 Root MSE 0.356 Angular [elem O Rotational Motion.ds 04/10/2017 09:00 AM Graph 1 _ L d 01 o O O 50_ Angular Position( rad ) I ”woo 01001 0 IV 01 o m (Siope) 6.37 :t 0.017 D (Y Intercept) -5.70 :r: 0.067 r 1.00 Mean Squared Error 0.0432 Root MSE 0.208 O Angular Velocitfl rad/s ) o 01 _- Rotational Motion.ds 04/10/2017 09:02 AM Graph 1 a) O u: C Angular Posifion( rad ) C B 3 0 30 25 ‘20 (I) E15 m (Slope) 19.8:t0.35 : b ( Y Intercept) -9.08 :I: 0.45 €10 r 0.996 0 Mean Squared Error 0.472 Root MSE 0.687 0'! Angular Vel Rotational Motion.ds 04/10/2017 09:04 AM Graph 1 140 120 ' Angular Position( rad _)_ 3 -h~ N A 0') oo o o o o O o O O O m ( Slope) 27.4 :t 0.11 b (Y Intercept) -14.5 :l: 0.15 r 1.00 Mean Squared Error 0.0405 Root MSE 0.201 Angular_\_/elocity( rad/s 2° * o 3 ...
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