Moment of inertia: development of rotational dynamics KIT for physics students

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1 IOP Conerence Series: Materias Science and Engineering PAPER OPEN ACCESS Moment o inertia: deveopment o rotationa dynamics KIT or physics students To cite this artice: D Muhayatiah et a 08 IOP Con. Ser.: Mater. Sci. Eng View the artice onine or updates and enhancements. This content was downoaded rom IP address on 5/0/09 at :6

2 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 Moment o inertia: deveopment o rotationa dynamics KIT or physics students D Muhayatiah *, H Y Suhendi, R Zakwandi, Y Dirgantara and M A Ramdani Program Studi Pendidikan Fisika, UIN Sunan Gunung Djati Bandung, J. AH. Nasution No. 05, Bandung 06, Indonesia Fakutas Sains dan Teknoogi, UIN Sunan Gunung Djati Bandung, J. AH. Nasution No. 05, Bandung 06, Indonesia *diahmuhayatiah@uinsgd.ac.id Abstract. Moment o inertia is one o the actors that inuences the motion o an object on the rotation motion. This study aims to determine the magnitude o the moment o inertia based on the orm by varying the mass and radius. Variations o orm in this study is a soid cyinder and a cyinder with a thick eather pate. Obtaining a constant vaue or the cyinder with a thick pate skin is made by comparing the vaue o moment o inertia between the soid cyinder and the moment o inertia in the cyinder with the skin o a thick pate. The research was done by roing the tubuar object on the incine with the height o h and the ange o θ. The motion o the object is then recorded using a sow motion and high resoution camera to get a good image. Variabe o height h and ange θ wi aect the acceeration o motion o the object. The motion in the soping path oows the aw o equivaence o mechanica energy so that the energy at the initia condition at the height o h and vo = 0 wi be equa to the ina state at h = 0 and v = max. The experimenta resuts show the moment o inertia or mass which is distinguished by average whie the cacuation resut was so there was a dierence o 5.3%. The resut o moment o inertia or the dierent radius is , whie the cacuation is so there is a dierence o 3.6%. The error o the resuts o moment o inertia is reativey sma, so it can be concuded that KIT rotationa dynamics can be appied in earning.. Introduction Moment o inertia is one o the actors that inuences the motion o the object on the rotation motion. The moment o inertia itse is deined as the measure o the inertia o the object to move in rotation. The discussion o the moment inertia in mechanics is contained in the chapter o the strong body mechanics so that to anayze the moment o inertia we must pay attention to the point coordinates in an object and the size o the object which in this case is inuenced by the size o the partice density in the object. Research on the determination o moment o inertia in various systems has been done. Shakoori examined the moment o inertia or ree ying vehice []. Kumar aso examined the appication and use o ywhee in engineering []. Eadkhong says that by omitting the eect o such riction, or a cyindrica pate rotated around the centra axis rom the other two experiments based on the reation between torque and anguar acceeration o rotationa motion and conservation o energy [3]. Kaupi aso said that experiments pay vita roe in scientiic argumentation. However, impications or pedagogy are generay negected []. Content rom this work may be used under the terms o the Creative Commons Attribution 3.0 icence. Any urther distribution o this work must maintain attribution to the author(s) and the tite o the work, journa citation and DOI. Pubished under icence by Ltd

3 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 The deveopment o moment properties o moment o inertia or earning is aso very necessary because o the imitations o experimenta aciities in schoos. Research by Kung indicates that the exposing students to aboratory methods and requiring imited uncertainty cacuations wi not aect their understanding o uncertainty - it takes a purposeu concept-based aboratory course to do that. Dierent ieds have dierent methods or cacuating, reporting, and comparing an experiment [5]. Moment o inertia itse is generay inuenced by the mass and radius o the system o objects. Based on the inuence o mass and radius and the shape o the system object then the moment o inertia o each object wi be dierent. Expaining the dierence in moment vaue o inertia can be done by conducting experiments invoving equipment representing various mass and radius. Warner states that in the ied o educationa to provide guidance by adopting that in schoos to support student earning, it must to be deined in a way that describes experiment as a too or probemsoving [6]. The use o moment o inertia experiments by using a cyindrica strong body system by distinguishing mass and radius can hep students in appying the concept with the appication and probem soving. Materias and methods The determination o the moment o inertia or the cyinder is mathematicay cacuated by distinguishing the mass o the system dm rdrd I I axis axis r 0 0 r rdrd r By substituting the mass vaue o the cyinder the above equation can be written to be: I mr With m is mass and r is the radius o the cyinder and the k vaue or the soid cyinder is ½. In the same way can be determined the vaue o the moment o inertia and the inertia constant in the hoow cyinder and the cyinder with the skin o thick pates. Reerring to the equation o moment o inertia on the cyinder it can be concuded that the moment vaue o inertia does not depend on the height o the tube. This research method is done by roing the tubuar object on the incine with the height o h and the ange o θ. Based on a physica quantity, such as a orce. I it is a vector, and has a meaning independent o any coordinate system [7]. Figure. The cyinder modes or experiment.

4 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 The motion o the object is then recorded using a sow motion and high resoution camera to obtain a good image. Figure. Object Path. Variabe o height h and ange θ wi aect the acceeration o motion o the object. The motion in the soping path oows the aw o conservation o mechanica energy so that the energy in the initia conditions (height h and vo = 0) wi be equa to the ina condition at h = 0 and v = max. Mathematicay can be ormuated: EM initia EM ina T initia V initia T ina V ina mvi Ii mghi mv I mgh 0 mgh i mv I 0 I mgh0 mv v r The above equation has a constraint at the time o observation because the anaytica vaue o the speed wi change caused by the acceeration o motion. So i it is substituted, it produces dierent vaues o moment o inertia and o course this is against the rues o motion in mechanics. Figure 3. Variations o objects Shapes. In the object motion the acceeration vaue obtained is reativey constant. This satisies the aw equation o Newton II which in that motion is not given outside orce and the mass o the moving object is ixed so that the acceeration o the object movement has a constant vaue. Then urther anaysis using Lagrange equation is as oows: 3

5 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 T mv I Remember that the genera equation or the moment o inertia is I = kmr where k is a constant that depends on the shape o the rotating object. So the above equation can be written to be: v T mv kmr r r T mv k T m cos cos k T m k V mgsin L m k mg sin L L t k g sin g k sin With L is the acceeration dimension with unit m / s. By using the anaysis we can deine the k vaue o an object experimentay. In genera, the image capture by using anaysis video tracker aims to get the object motion acceeration vaue. Ramdhani says that a ot o activities previousy carried out manuay (non-computer) are then aciitated by [8]. Figure. Video with tracker anaysis.

6 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 To ind out how the orm inuences in determining the vaue o the moment o inertia, the object is divided into three orms: hoow tube, soid tube and ayered tube. Factors aecting moments o inertia other than orm are mass and radius. This experiment was carried out using the same trajectory and variations o mass and radius into sizes. The shape variation is intended to observe how the eect o uneven distribution o mass on the motion o objects by rotation. Variations o orm in this study is a soid cyinder and a cyinder with a thick eather pate. The vaue o k or the tube with the skin o a thick pate is made by comparing the vaue o moment o inertia between the soid cyinder and the moment o inertia in the cyinder with the skin o a thick pate. The ast stage o this study is to compare the vaue o the constant o moment o inertia rom experiment with the resut o cacuation. Mathematicay the cacuation o error vaue is as oows: khitung 00% k reerensi The vaue o this measurement error to ind out the accuracy o the experimenta too. Krisnan states that the estimation is ikey to be vaid and acceptabe or the cacuation o torque requirement o the turn tabe in moment o inertia [9]. 3. Resuts The experimenta resuts by roing the cyinder with the same mass o 0.68 kg and the ange o sope 6. in the incined pane obtained data presented in tabe Radius (m) Tabe. Error or radius variation. a (m/s ) I= ½ g sin mr I mr Eror % 0,055,7805 0,0005 0, ,5 0,03,8389 0, ,0009, 0,0385,7706 0,0005 0, ,7 0,09,7863 0, ,00007,89 Average 0,0005 0, ,3 Tabe shows that the vaue o the moment o inertia or dierent types o cyinders radius shows a sma comparison o the vaue o moments o inertia mathematicay based on counting. In the experiment by roing the cyinder with radius = 0.06 m and the ange o sope 6. on the incine is presented in tabe. Tabe. Error or Mass Variation. Mass a (m/s (kg) ) I= ½ mr g sin Eror I mr % 0,088, ,0008 0, ,70 0,09,885 0, ,0009,08 0,099, , ,0000 0,55 0,38,7976 0, ,00039,35 Average 0, ,0000,67 Based on the data in tabe it is seen that the greater mass o the object the greater vaue o the moment o inertia. The orm o correation between radius with moment o inertia both moments o inertia o mathematica cacuation with the one generated by experiment is shown in igure. 5

7 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 0,0003 0,000 0, ,0 0,0 0,06 Figure 5. Graph o R towards I. In igure 5 it is seen that the resuting graphic tendency is exponentia between radius and moment o inertia. Lee (08) stated in his research that it indicates that the riction orce and torque can be in a range or the moment inertia [0]. For the cyinder with thick skin can be mathematicay anayzed by equation I R h 0 0 r I r dm r dm R r drdh r r drdh I hr I= ½ mr Expon. (I= ½ mr) Linear (I= ½ mr) h R 0 h R For the vaue o ρ is zero because there is no mass distribution on the part. Thereore by reducing the equation above we can write a new expression or the hoow cyinder with thick skin as: I h R In this experiment, to show the correation above, then a comparison between the radius o soid object and hoow cyinder with thick skin is done. R R Tabe 3. Moment o inertia resuts in hoow cyinder with thick skin. Mass (g) Jari-Jari (m) Perbandingan Moment Veocity (m/s) R in R out Inersia 5, - 38,,3057,9 5, 6,35 38, 0, ,7-63,5,0689, ,7 38, 63,5,06 63,7-76,,806,06 63,7 6,35 76,, ,0-0,6,5 0,986 96,0 50,8 0,6, The resuts obtained rom the motion system indicate that the vaue o the moment o inertia in the soid cyinder is ess than the moment vaue o inertia possessed by the cyinder with thick pate on the outer radius and the same mass. This is shown by the speed o motion o the system in the horizonta pane. 6

8 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 Margot states that the raction o the moment inertia that corresponds to the outer, which can be used to estimate the size o the core [].. Discussion Based on the resuts obtained in tabe, the greater the radius the greater the vaue o the moment o inertia. This is because mathematicay it can be ormuated that I r. The moment o inertia o mathematica cacuations with experimenta resuts shows a sight error with an average error rate o 5.3%. This is in accordance with the statement by Gierak in his research in a imited operating surace o the media and a decrease in the eiciency o processing []. Furthermore in tabe it can be seen that the correation between moment o inertia with mass is inear. Mathematicay can be expressed as I m. The vaue o moment o inertia based on mathematica cacuations based on experimenta resuts using tracker shows an error rate o.67%. In ine with Tahmasebi's research that simuation methods hep to compute the estimated inertia or mass continuousy [3]. Based on the reativey sma error rate indicates that the rotation dynamics kit can be used as an experimenta too or earning the moment o inertia. Grober states that Emphasis is put on theory experiment as a structura to promote students' construction o knowedge and conceptua understanding []. Sea aso stated in his research that direct eedback to experimenta actions in orm o dierent representations aows or comparison to theoretica principes and predictions and thereore is supposed to intensiy the theory-experiment interactions and aso to increase students conceptua understanding in education [5]. The merger o two orms o reationship, i.e. mass and radius can be written that I mr. Heed expains simiar uncertainty in the moment o inertia vaue as dierent core properties (mass, radius) [6]. To baance this orm o equaity, a constant is deined as I = k mr. The equation shows the genera equation o the moment o inertia. The vaue o k depends on the shape o the rotating object. Based on the measurement resuts and cacuations contained in tabe and tabe using the equation o motion the object gives resuts cose to the theoretica cacuations. Use o equations g sin k obtained vaue o the constant o moment o inertia equa to 0,555 with error equa to 3,0% vaue o constant which is stated in reerence. Gunadin and aso Samet say or retrieving the knowedge, severa research propose a ot o retrieva methods and modes or extraction, buid an ontoogy, deveoping new corpuses, and so on [7], [8]. 5. Concusion KIT rotationa dynamics that preer the determination o moment o inertia o the strong body system can expain experimentay about moment o inertia. The error rate o experimenta equipment is reativey sma so it is easibe to be appied in earning. Acknowedgements Thank you so much to the Center or Research and Deveopment or unding and supporting the research. Reerences [] A Shakoori, A V Betin and D A Betin 06 Comparison o three methods to determine the inertia properties o ree-ying dynamicay simiar modes J. Eng. Sci. Techno.(0) pp [] S Kumar and J Das 03 Appication and Use o Fywhee in Engineering: Overview Int. J. Adv. Sci. Eng. Techno pp [3] T Eadkhong, R Rajsadorn, P Jannua and S Danworaphong 0 Rotationa dynamics with 7

9 3rd Annua Appied Science and Engineering Conerence (AASEC 08) IOP Con. Series: Materias Science and Engineering (08) 00 doi:0.088/ x/3//00 Tracker Eur. J. Phys. 33(3) pp [] J Koupi and V Vícha 0 Simpe phenomena, sow motion, surprising physics Phys. Educ () pp [5] R L Kung 005 Teaching the concepts o measurement: An exampe o a concept-based aboratory course Am. J. Phys. 73(8) pp [6] C K Warner, C V Be, A L Odom and C K Warner 08 Deining Technoogy or Learning : Cognitive and Physica Toos o Inquiry () [7] D Nanto, A N Aini and D Muhayatiah 07 Android worksheet appication based on discovery earning on students achievement or vocationa high schoo: Mechanica behavior o materias topics in AIP Conerence Proceedings 88 [8] M A Ramdhani and E R Wuan 0 The Anaysis o Determinant Factors In Sotware Design For Computer Assisted Instruction Int. J. Sci. Techno. Res. (8) pp [9] R Hari Krishnan, V Devanandh, A K Brahma and S Pugazhenthi 06 Estimation o mass moment o inertia o human body, when bending orward, or the design o a se-transer robotic aciity J. Eng. Sci. Techno. () pp [0] Y Lee 08 Tracking Design o an Omni-Direction Autonomous Ground Vehice by Hierarchica Enhancement Using Fuzzy Second-Order Variabe Structure Contro 0 no. September, pp. [] J L Margot, S J Peae, S C Soomon, S A Hauck, F D Ghigo, R F Jurgens, M Yseboodt, J D Giorgini, S Padovan and D B Campbe 0 Mercury s moment o inertia rom spin and gravity data J. Geophys. Res. Ocean. 7(0) pp. [] P Gierak 08 The manipuator too state cassiication based on inertia orces anaysis Mech. Syst. Signa Process. 07 pp. 36 [3] M Tahmasebi, M Maiah, M Gohari and R Abd Rahman 07 Vibration suppression o sprayer boom structure using active torque contro and iterative earning. Part I: Modeing and contro via simuation JVC/Journa Vib. Contro, no. August [] S Gröber, P Kein and J Kuhn 0 Video-based probems in introductory mechanics physics courses Eur. J. Phys. 35(5) [5] B Sea and K C Pii 007 Ac ce d M us p [6] R Heed 0 Constraining Saturn s core properties by a measurement o its moment o inertia - Impications to the Cassini Sostice Mission Astrophys. J. Lett.735() pp. [7] I C Gunadin 07 Transient Stabiity Improvement Using Aocation Power Generation Methods Based o n Moment Inertia no ICELTICs pp. 7 5 [8] C Samet, A Rahman, M A Ramdhani and W Dharmaaksana 06 Custering the verses o the hoy qur an using K-means agorithm Asian J. In. Techno. 5() pp