1 Kinesiologia Slovenica, 14, 3, 5 14 (28) Faculty of Sport, University of Ljubljana, ISSN Matej Supej* Milan Čoh USING THE DIRECTION OF THE SHOULDER S ROTATION ANGLE AS AN ABSCISSA AXIS IN COMPARATIVE SHOT PUT ANALYSIS UPORABA SMERNEGA KOTA RAMENSKE OSI ZA ABSCISO PRI PRIMERJALNIH ANALIZAH META KROGLE ABSTRACT As a rule, independent and comparative analyses of shot put data either use time-series data or generate timedependent data. Thus, a direct time-dependent comparison of two or more competitors can only be made in a limited period of time due to differences in the shot put technique and execution. We hereby propose a method in which the direction of the shoulder s rotation angle is used as an abscissa axis as a useful tool, since experts and athletes find this method easier to conceive and apply in their field work. To demonstrate the practicability of this new abscissa, we measured the 3-D kinematics of two morphologically different elite shot putters. We demonstrated a monotonic increase in the direction of the shoulder s rotation angle in a rotational technique, which serves as a basis for the application. Furthermore, the following major parameters are representatively shown: shot height, angular velocity in the elbow of the release arm, the direction of the ankles rotation angle and absolute shot velocity. To allow a comparison, all the parameters are presented in a time- and angle-dependent manner. It was established that the new data analysis method not only brings additional benefits of data harmonisation and an easier mental conception, but also reveals new information that remains obscured in a temporal harmonisation. Key words: analysing methodology, shot put, direction of the shoulder s rotation angle, 3-D kinematics, comparative analysis POVZETEK Navadno se pri samostojnih in primerjalnih analizah podatkov suvanja krogle uporablja časovno zaporedje podatkov oz. prikaz podatkov v odvisnosti od časa. Na tak način je neposredna primerjava dveh ali več tekmovalcev v časovni odvisnosti omejena na kratko območje zaradi razlik v tehniki in izvedbi. V pomoč predlagamo uporabo uskladitve podatkov glede na smerni kot ramenske osi, ki je za strokovnjake in atlete bolj predstavljiva in lažje uporabljiva na terenu. Za prikaz uporabnosti»nove«abscise smo naredili meritve 3D kinematike dveh morfološko različnih vrhunskih metalcev krogle. Pokazali smo monotonost naraščanja smernega kota ramenske osi pri rotacijski tehniki, kar je osnova za uporabnost. Poleg tega reprezentativno prikazujemo še naslednje pomembne parametre: višina krogle, kotna hitrost v komolcu izmetne roke, smerni kot gležnjev in absolutna hitrost krogle. Vsi parametri so za primerjavo prikazani tako v časovni kot kotni odvisnosti. Izkaže se, da ima nova metoda analiziranja podatkov ne le prednosti pri usklajevanju podatkov in predstavljivosti, temveč tudi nosi nove informacije, ki v časovni usklajenosti ostanejo skrite. Ključne besede: metodologija analiziranja, met krogle, smerni kot ramenske osi, 3D kinematika, primerjalna analiza Faculty of Sport, University of Ljubljana, Ljubljana, Slovenia *Corresponding author: University of Ljubljana, Faculty of Sport Gortanova 22, 1 Ljubljana, Slovenia Tel.: Fax:
2 6 The direction of the shoulder s rotation angle Kinesiologia Slovenica, 14, 3, 5 14 (28) INTRODUCTION Evaluating a shot put performance is very simple as the distance thrown is the only result that counts. The distance thrown is defined primarily by the path on which force is applied to the shot, which is manifested in the release velocity, the angle of release and the height of release (Stepanek, 1989; Palm, 199; Gemer, 199; Bartonietz, 1994; Oesterreich, Bartonietz, & Goldmann, 1997; Luhtanen, Blomqvist & Vanttinen, 1997; Lanka, 2; Hubbard, Neville & Scott, 21; Linthorne, 21; Rasmussen, 25). However analysing a shot put technique is completely different and can be very challenging given that (even though it is relatively limited in the available space and time) shot put consists of a complex 3-D motion. This complexity of movement that produces force on the shot and the limited space and time are the factors that make an analysis a laborious task for coaches, experts and scientists. In particular, a comparison of competitors (as one of the most commonly applied analysis methods) is also hindered, especially when it is difficult to set up a precise implementation model. An identical situation occurs with shot put since large differences in the movement action can be produced solely by morphological and anthropometrical differences between the competitors. For example, the relative shot mass in relation to an athlete s mass can be a highly influential factor from the mechanical point of view and, accordingly, also from the technique point of view (Bartonietz, 1994; Bartlett, 2). Similar effects can be produced by body height (Bartlett, 2; Linthorne, 21) and so on. These are the reasons for frequently applying comparative analyses to identify athletes strengths and weaknesses. The problem of comparative analyses is in harmonising data concerning individual throws. Most often the harmonisation method is based on a time axis; however, this is not the optimal solution. A slight difference in the initial phase, especially when the movement is slow, can delay the situation and thus jeopardise the objectivity of comparison. For example, at the moment one athlete is still completing the first double-support phase; the other has already started the single-support phase (Luhtanen et al., 1997). For this reason, some prefer to use the harmonisation of the time axis in relation to the point of release; i.e. the time the shot is released from the palm (Palm, 199; Goss-Sampson & Chapman, 23). The reason for this mainly lies in the fact that the final release phase is considered to be more important. Nevertheless, some phases are still poorly synchronised due to differences in the movement action. Owing to this problem of harmonising data on the time axis it is reasonable to consider spatial harmonisation. Unfortunately, the throwing action is performed within a relatively limited space making it almost impossible for the analysis or interpretation to rely on the place of action, even though the shot movement trajectory is one of the main parameters (Linthorne, 21). An even more awkward situation occurs when experts or scientists information or advice to athletes relies on the place or time of an event. Therefore, in both practice and science, either a different notional concept or a division into phases is used, e.g. the first double-support phase, the single-support phase, the flight phase etc. (Luhtanen et al., 1997). A problem arises when the time scale that is used in science needs to be co-ordinated with the terminology used by professionals. Hence, we believe that a new axis should be introduced on which both professionals and scientists can rely. One way we propose to resolve this problem is to introduce a polar angle of the body s rotation as the harmonisation axis, as the body s rotation can be easily conceived of by athletes and coaches/professionals and is at the same time a scientifically- and uniquely-defined parameter. How the new method is used will be demonstrated by measuring the 3-D kinematics of two elite shot putters. METHODS Procedures The introduction of a new data analysis method for comparative analyses is based on a directional vector of the shoulder axis of the body and its inclination from the direction of the field sector. The following vectors are required to calculate it:
3 Kinesiologia Slovenica, 14, 3, 5 14 (28) The direction of the shoulder s rotation angle 7 n normal of the plane of ground i.e. the throwing circle (r = m); sr spatial vector of the right shoulder; sl spatial vector of the left shoulder; and f vector pointing towards the direction of the throw along the middle of the field sector. The vector multiplication of n and (sr-sl) results in a vector parallel to the plane of the throwing circle and pointing in the direction of the body s rotation. The angle of the rotation is a result of the dot product of the vectors n (sr-sl) and f. The result is an equation for the direction of the body s rotation angle: fi = arccos( (n (s r -s l )) f / ( n s r -s l )). (1) Given that a shot putter makes more than one turn, a short programme is required to establish when the angle passes over from one quadrant to another so as to prevent the angle shifting from 18 to -18. Zero is set at a point rotated towards the direction of the throwing field in the last turn at the release point. Once an appropriate parameter of the body s rotation is obtained, all other calculated parameters can be presented in relation to the angle of rotation and not only in relation to the time axis. The application will be exemplified by the following selection of parameters: absolute shot velocity, shot height, angular velocity in the elbow of the release arm and the direction of the ankles rotation angle, which is calculated by analogy to the direction of the body s rotation angle. To calculate the parameters, independent routines were programmed by Matlab software and, where appropriate, they were smoothed with adequate cut-off frequencies and the orders of the Butterworth filter. The parameters were always calculated from raw data, while some of them were filtered subsequently. In all cases, both versions of the parameters are presented those calculated from the raw data and the filtered ones. As the parameters are always presented in a comparative context, the zero time point was set at the shot release while the zero point of the direction of the body s rotation angle was set at the moment the athlete s shoulder axis is rotated towards the direction of the sector. Participants To demonstrate the application of the newly proposed abscissa in analysis, we used data acquired from measuring two elite shot putters (M.V. age 28, height 1.95 m, mass kg, BMI (body mass index) = 44.5; personal record 2.76 m; H.A. age 26, height 1.85 m, mass 12.2 kg, BMI = 35.1, personal record 2.2 m) in May, 25 at an international athletic meeting held in Slovenska Bistrica, Slovenia. Instruments Recordings were made with two fixed and synchronised camcorders (SONY DVCAM DSR- 3 PK), where the angle between the optical axes of the two camcorders was about 9. The camcorder frequency was 5 Hz and the resolution 72 x 576 pixels. The analysed area of the circle was calibrated with a 1 m x 1 m x 2 m reference scaling frame and the calibration was based on eight reference corners. The length of the analysed movement was defined by the x axis, the height by the y axis and the depth by the z axis.
4 8 The direction of the shoulder s rotation angle Kinesiologia Slovenica, 14, 3, 5 14 (28) The APAS 3-D software (Ariel Dynamics Inc., San Diego, Ca.) was applied to determine the points on the digital video recordings and transform the 2x 2-D data into 3-D data. The 15-segment model of the shot putter s body was digitised and defined by 18 reference points. The eighteenth point was defined by the centre of the shot. The segments of the model represented parts of the body, linked with point-like joints. The masses and centres of gravity of the segments as well as the centre of gravity of the body were calculated by the anthropometric system (Dempster, 1955). The competitors used their right arm to put the shot. Six attempts of each competitor were recorded and only the best throw was included in the final analysis, 2.3 m and 19.6 m for M.V. and H.A., respectively. RESULTS The basis of an effective application of the direction of the shoulder s rotation angle as an abscissa axis is its time-dependant monotonic increase. As the shot putter starts from an extreme position and is repeatedly turning in the same direction until the moment of releasing the shot, the parameter fulfils the basic condition, as shown in Figure 1. It is obvious that the increase is not regular but is slower at the beginning because the athletes turn more slowly. Towards the final phase, from the time of -.4 s on, they turn more quickly. -2 fi ( ) t (s) Figure 1: The time-dependent direction of the shoulder s rotation angle for two shot puts. The vertical line shows the point of release At first glance, Figure 1 shows no major differences between the athletes, which could imply that the introduction of the new abscissa will yield no new information in terms of a comparison of athletes. In truth, this only occurs at the beginning and at the end of the diagram, which is also seen in the video frames in Figure 2 (the upper two and bottom two frames). Nevertheless, the differences in the mid section are relatively large, ranging from -1.1 s to -.1 s, i.e. from about -5 to -1, representing the major part of preparation for the release. For example, at the time of -.4 s (Figures 1 and 2) the difference in rotation equals almost 6, i.e. one-sixth of a full turn. All of the above already shows the added value of the introduced new abscissa in the comparative context, bearing in mind that a temporal harmonisation would allow the observation of parameters in a completely different execution phase.
5 Kinesiologia Slovenica, 14, 3, 5 14 (28) The direction of the shoulder s rotation angle 9 Figure 2: Video frames at three selected times for the two shot putters: left H.A. (result: 19.6 m), right M.V. (result: 2.3 m) To start with, a simple parameter of shot height as shown in Figure 3 reveals a clear-cut difference between the time-dependent and angle-dependent data presentations. As the sample of subjects consists of two morphologically quite different athletes, the diagrams are much more interesting. We can see that the difference between the taller and the shorter athletes in terms of shot height is considerable but,.5 of a second before the release, both shot heights are within a range of a few centimetres. The upper diagram reveals that this happened at approximately 33 before the athletes rotated towards the direction of the field sector. The difference again started to show at about one-quarter of the turn before the zero angle. A more detailed observation reveals that the difference started to increase even more quickly from the zero angle onward; namely, in the very final phase of the release.
6 1 The direction of the shoulder s rotation angle Kinesiologia Slovenica, 14, 3, 5 14 (28) shot height (m) fi ( ) shot height (m) time (s) Figure 3: Shot height depending on the direction of the shoulder s rotation angle (above) and on time (below) for the two shot puts. The vertical dashed line shows the point of release Even more interesting is the observation of differences in the angular velocity in the elbow of the right release arm used by both shot putters (Figure 4). The time-dependent diagram, i.e. the lower diagram of Figure 4, shows the delay in the angular velocity of both competitors. However, it is established that both athletes extended their elbows almost at almost the same speed in relation to the body s rotation ( the direction of the shoulder s rotation angle) as the curves are relatively well compatible from -135 to 45 (Figure 4, the upper diagram). The division of the throwing action into phases (e.g. the first double-support phase, the singlesupport phase, the flight phase etc.) is clearly manifested in the direction of the ankles rotation angle (Figure 5). Each time both legs are in contact with the ground, the angle remains more or less the same. If the two athletes are compared in terms of temporal harmonisation, the phases follow each other in a very similar way. The rotation in the double-support phase and the first single-support phase of H.A. (result: 19.6 m) in the time period from zero to -.6 s is 15 to 55 more than with M.V. (result: 2.3 m). Other phases are very similar and only exceptionally slightly exceed a difference of 2. A comparison of the body s position in relation to phases and an angle-dependent presentation of the direction of the ankles rotation angle reveal even larger differences, ranging from about -45 to -11 (Figure 5, below). The largest difference is seen between the angles of about -31 and -18, indicating the considerably different technical implementation of this segment.
7 Kinesiologia Slovenica, 14, 3, 5 14 (28) The direction of the shoulder s rotation angle 11 elbow angular vel. (rad s -1 ) fi ( ) elbow angular vel. (rad s -1 ) t (s) Figure 4: Angular velocity in the elbow of the right release arm for the two shot puts, depending on the direction of the shoulder s rotation angle (above) and on time (below). The full and dashed lines show the filtered data, while the circles and diamonds show the unfiltered data. The vertical dashed line shows the point of release. 4 ankles angle ( ) fi ( ) 4 ankles angle ( ) time (s) Figure 5: The direction of the ankles rotation angle for the two shot puts depending on the direction of the shoulder s rotation angle (above) and on time (below)
8 12 The direction of the shoulder s rotation angle Kinesiologia Slovenica, 14, 3, 5 14 (28) abs vel. (m s -1 ) fi ( ) abs vel. (m s -1 ) time (s) Figure 6: The absolute shot velocity in the two shot puts depending on the direction of the shoulder s rotation angle (above) and on time (below). The full and dashed lines show the filtered data, while the circles and diamonds show the unfiltered data. The difference in the presentation can also be seen in the selected parameter: absolute shot velocity (Figure 6). A closer observation of the time-dependent diagram (the one below) shows that the curves split at the time of -.22 s and never join again. According to this diagram, the greatest advantage of shot putter M.V. (result: 2.3 m) is the fact that he started increasing the shot velocity.4 s earlier than A.H. (result: 19.6 m). However, the upper diagram of Figure 6 provides different information: the first important difference occurs between the angles of -11 and -9 and the second in the very final phase of the release, between the angle of 1 and the point of release. DISCUSSION It has been demonstrated that the direction of the shoulder s rotation angle as a new element of shot put analyses provides a very useful tool. The basic idea was to relate the angle to the body s centre of gravity; however, the latter is only a point and has no direction whatsoever. Consequently, in the first research phase, the vector linking the point of the body s centre of gravity and the shot was investigated. It was established that the direction of this vector was not relevant. Moreover, the points can even position themselves one above the other, resulting in unwanted singularities and serious errors. The second option was either the direction of the shoulder s rotation angle or the direction of the hip s rotation angle. We chose the former, even though at first glance the hip axis appears to be a better choice because its behaviour is more similar to that of the body s centre of gravity. This choice was made for the following reasons:
9 Kinesiologia Slovenica, 14, 3, 5 14 (28) The direction of the shoulder s rotation angle 13 for coaches, the shoulder axis is more visible and easier to conceive. In contrast, the hip axis is generally burdened by larger errors because in the most frequently used 3-D kinematic methods, where a camera system is applied, the determination of the hip joint is made difficult by the thickness of the tissue covering it. As already mentioned in the results, the direction of the shoulder s rotation angle shows a monotonic increase caused by the specific nature of the shot put. Thus, in mathematical terms it is a suitable parameter (Figure 1). However, the non-proportionate increase in the angle or rotation of the athlete shows that the transformation from temporal to spatial dimensions is harder to imagine for experts, thus bringing value added to the angle-based approach. Although this is not explicitly seen in Figure 1, it is very important that temporal harmonisation causes a great delay in the body s rotation (Figure 2). This hinders a detailed comparison of the shot put technique, even though it provides the information that the duration of an individual action differs from athlete to athlete. The examples in Figures 3 to 6 confirm that the introduction of the direction of the shoulder s rotation angle as an abscissa axis is highly valuable. In data analysis, it can be helpful in many ways. It improves one s conception of the phase during which the action took place and this is clearly demonstrated in the example of shot height (Figure 3). In addition, harmonisation in comparative analyses is different because new information can be used. It was thus established that the angular velocity in the hip joint of both study subjects was very similar with regard to their body position, despite the fact that it was delayed. This new approach allows us to observe differences in the execution of technique in some parameters, even though this cannot be seen on a time scale, e.g. the position of the ankles in the diagrams of Figure 5. Last but not least, with the new functionality we can better define the fractions of the throwing action in which the major differences occur and determine why one athlete is more successful than the other, as is also shown by the diagrams in Figure 6. It can be asserted that the observation of time-dependent parameters is important due to the definition of physical parameters. It is also true that people, including experts, athletes and scientists, are used to dealing with parameters from the temporal perspective. Therefore, temporal harmonisation will remain a major element of analyses. In spite of the above, it can be argued that in practical field work it is easier to observe the technique and simpler to imagine concepts if they are supported by spatial co-ordinates or, in our case, the rotation of the body. Moreover, this method of presenting parameters in a comparative analysis yields many new and important pieces of information. Even though the new data analysis method has not yet been tested on the linear shot put technique (Stepanek, 1989), we anticipate that this new approach is also applicable there. Furthermore, the last half of the turn can probably be efficiently harmonised, allowing for a consideration of hypothetical differences between the linear and the rotational techniques. This further increases the applicability of the new insight into data emerging from comparative analyses, as these two techniques are difficult to harmonise in time. In fact, when applying the new method, we have to shift our observation focus to the rotation of the shoulder axis. Theoretically, the only drawback of the new method is the limited accuracy of the measurement of the shoulder axis rotation. However, in view of the development of technology, we claim that this factor is becoming less important every day.
10 14 The direction of the shoulder s rotation angle Kinesiologia Slovenica, 14, 3, 5 14 (28) ACKNOWLEDGMENTS This study was supported in part by a grant from the Slovenian Research Agency and the Slovenian Foundation for the Co-financing of Sport Organisations. REFERENCES Bartlett, R. (2). Principles of throwing. In V. Zatsiorsky (Ed.), Biomechanics in Sport: Performance Enhancement and Injury Prevention (pp ), Oxford: Blackwell Science Ltd. Bartonietz, K. (1994). Rotational shot put technique: Biomechanic findings and recommendations for training. Track and Field Quarterly Review, 93 (3), Bartonietz, K., & Borgström, A. (1995). The throwing events at the World Championships in Athletics 1995, Göteborg Technique of the world s best athletes. Part 1: Shot put and hammer throw. New Studies in Athletics, 1 (4), Hubbard, M., Neville, J., & Scott, J. (21). Dependence of release variables in the shot put. Journal of Biomechanics, 34, Gemer, G. (199). Overview of the Shot Put Technique. New Studies in Athletic, 5 (1), Goss-Sampson, M., & Chapman, M. (23). Temporal and kinematic analysis of rotational shot put technique. Journal of Sports Sciences, 21, Lanka, J. (2). Shot Putting. In V. Zatsiorsky (Ed.), Biomechanics in Sport: Performance Enhancement and Injury Prevention (pp ), Oxford: Blackwell Science Ltd. Linthorne, N. (21). Optimum release angle in the shot put. Journal of Sports Sciences, 19, Luhtanen, P., Blomqvist, M., & Vanttinen, T. (1997). A comparison of two elite shot putters using the rotational shot put technique. New Studies in Athletics, 12 (4), Lukes, D. (1989). Rotation shot put for beginners. Track and Field Quarterly Review, 3, 9-1. Oesterreich, R., Bartonietz, K., & Goldmann, W. (1997). Rotational technique: A model for the long-term preparation of young athletes. New Studies in Athletics, 12 (4), Palm, V. (199). Some biomechanical observations of the rotational shot put. Modern Athlete and Coach, 28 (3), Rasmussen, B. (25). Spin to Win. Part 1: Introduction to Rotational Shot Put. Accessed on 6 May 27 from Stepanek, J. (1989). Comparison of glide and the rotation technique in the shot put. In: Tsarouchas, L. (ed). Biomechanics in Sport. In Proceedings of the V International Symposium of the Society of Biomechanics in Sport (pp ), Athens: Hellenic Sports Research Institute, Olympic Sports Centre of Athens.
Available online at www.sciencedirect.com Procedia Engineering 34 (2012 ) 790 794 9 th Conference of the International Sports Engineering Association (ISEA) Preliminary study of Accuracy and reliability
Loughborough University Institutional Repository The margin for error when releasing the high bar for dismounts This item was submitted to Loughborough University's Institutional Repository by the/an author.
TECHNICAL NOTES INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1985, 1, 73-77 Biomechanical Analysis of a World Record Javelin Throw: A Case Study Robert j. Gregor University of California, Los Angeles Marilyn
2A/2B BIOMECHANICS 2 nd ed. www.flickr.com/photos/keithallison/4062960920/ 1 CONTENT Introduction to Biomechanics What is it? Benefits of Biomechanics Types of motion in Physical Activity Linear Angular
Loughborough University Institutional Repository Why do high jumpers use a curved approach? This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: TAN,
ANALYSIS OF THE KINETIC STRUCTURE OF THE SMASH-SHOOT IN VOLLEYBALL M.Dodig, University of Rijeka, Faculty of Maritime, Rijeka, Croatia INTRODUCTION Starting from the recognition that the contribution and
Energy and Power in (Sports) Biomechanics Department Center of for Sport Sensory-Motor and Exercise Interaction Science SPORTSCI 306 Technique Anvendt Assessment Biomekanik Uwe Uwe Kersting Kersting MiniModule
VCE PHYSICAL EDUCATION UNIT 3 AOS 1 KEY KNOWLEDGE 3.1.4 BIOMECHANICAL PRINCIPLES FOR ANALYSIS OF MOVEMENT (PART 1) Presented by Chris Branigan Study design dot point: Biomechanical principles for analysis
Lab 2 - Introduction to Motion 3 Name Date Partners LAB 2: INTRODUCTION TO MOTION Slow and steady wins the race. Aesop s fable: The Hare and the Tortoise Objectives To explore how various motions are represented
Available online at www.sciencedirect.com Procedia Engineering 34 (2012 ) 772 777 9 th Conference of the International Sports Engineering Association (ISEA) Mechanical energy transfer by internal force
DO-TH 10/12 The optimal angle of Release in Shot Put Alexander Lenz arxiv:1007.3689v2 [physics.pop-ph] 26 Jul 2010 Institut für Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany and Institut
Name Date Partners L02-1 LAB 2 - ONE DIMENSIONAL MOTION OBJECTIVES Slow and steady wins the race. Aesop s fable: The Hare and the Tortoise To learn how to use a motion detector and gain more familiarity
Kinesiology 201 Solutions Kinematics Tony Leyland School of Kinesiology Simon Fraser University 1. a) Vertical ocity = 10 sin20 = 3.42 m/s Horizontal ocity = 10 cos20 = 9.4 m/s B Vertical A-B (start to
Estimating Body Segment Motion by Tracking Markers William C. Rose, James G. Richards Department of Kinesiology and Applied Physiology, University of Delaware Corresponding author: William C. Rose University
International Conference on Education, Management and Computing Technology (ICEMCT 05) Numerical Analysis and Position Strategies of Tug-of-war Yizhou TANG, Xin LIN,a,* School of Economics and Management,
Cutnell/Johnson Physics Classroom Response System Questions Chapter 9 Rotational Dynamics Interactive Lecture Questions 9.1.1. You are using a wrench in an attempt to loosen a nut by applying a force as
Rothwell Bronrowan email@example.com This paper begins with an example chosen to indicate the difficulties associated with determining which of several plausible, alternative frames of reference - if
Loughborough University Institutional Repository Maximising somersault rotation in tumbling This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: KING,
LABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS This laboratory allows you to continue the study of accelerated motion in more realistic situations. The cars you used in Laboratory I moved in only
Journal of Theoretics Guest Commentary Volume 6-4, Aug/Sept 2004 From Space-time to Space Amrit Sorli, Kusum Sorli SpaceLife Institute, Podere San Giorgio 16, 53012 Chiusdino (SI), Italy www.directscientificexperience.com
Marble Launch Experiment Purpose The intent of this experiment is to numerically trace the path of a marble launched into the air at an angle in order to observe the parabolic nature of the trajectory.
Low-level Fall Simulation: Toddler Falling From Chair R. J. Reimann Professor Emeritus of Physics Boise State University 11 June 2012 (rev. 7/9/2013) This simulation was generated using Working Model software
CHAPTER 11:PART 1 THE DESCRIPTION OF HUMAN MOTION KINESIOLOGY Scientific Basis of Human Motion, 12 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State
Quantitative Description of Robot-Environment Interaction Using Chaos Theory 1 Ulrich Nehmzow Keith Walker Dept. of Computer Science Department of Physics University of Essex Point Loma Nazarene University
Casting Physics Simplified Part Two Part one of this paper discussed physics that applies to linear motion, i.e., motion in a straight line. This section of the paper will expand these concepts to angular
Rotating objects tend to keep rotating while non- rotating objects tend to remain non-rotating. In the absence of an external force, the momentum of an object remains unchanged conservation of momentum.
CHAPTER 4: Linear motion and angular motion Practice questions - text book pages 91 to 95 1) Which of the following pairs of quantities is not a vector/scalar pair? a. /mass. b. reaction force/centre of
Proceedings An Empirical Model of Aerodynamic Drag in Alpine Skiing Ola Elfmark 1, * and Lars M. Bardal 2, * 1 Department of Civil and Environmental Engineering, Norwegian University of Science and Technology,
v (m/s) a (m/s^2) 1-D Motion: Free Falling Objects So far, we have only looked at objects moving in a horizontal dimension. Today, we ll look at objects moving in the vertical. Then, we ll look at both
Impulse Momentum and Jump PRELAB IMPULSE AND MOMENTUM. In a car collision, the driver s body must change speed from a high value to zero. This is true whether or not an airbag is used, so why use an airbag?
HPER K530 Mechanical Analysis of Human Performance Fall, 2003 Dapena MID-TERM Equations: S = S 0 + v t S = S 0 + v 0 t + 1/2 a t 2 v = v 0 + a t v 2 = v 2 0 + 2 a (S-S 0 ) e = h b /h d F CP = m v 2 / r
Back to Basics Section D: Ion Optics CHAPTER D3 TOF ION OPTICS TABLE OF CONTENTS QuickGuide...399 Summary...401 Background...403 EquationsofMotionofIons...403 Resolution...405 Reflectron...407 Comparison
LABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS In this laboratory you continue the study of accelerated motion in more situations. The carts you used in Laboratory I moved in only one dimension.
Scientific Examination of Relativistic Velocity and Acceleration Addition Copyright 2010 Joseph A. Rybczyk Abstract Direct comparison of the millennium relativity relativistic velocity and acceleration
From the SelectedWorks of Vildyan Yanbikov 2015 Experimental check on the validity of the special theory of relativity Vildyan Yanbikov Available at: https://works.bepress.com/vildyan_yanbikov1/21/ Experimental
Abstract CRITERIA FOR SELECTING AREAS FOR ORIENTEERING MAPS Dusan Petrovic University of Ljubljana, Faculty of Civil and Geodetic Engineering, Ljubljana, Slovenia firstname.lastname@example.org The paper
PHYS-101 LAB-02 One and Two Dimensional Motion 1. Objectives The objectives of this experiment are: to measure the acceleration due to gravity using one-dimensional motion, i.e. the motion of an object
An Adaptive Autoguider using a Starlight Xpress SX Camera S. B. Foulkes, Westward, Ashperton, Nr. Ledbury, HR8 2RY. Abstract The acquisition of very faint deep sky objects, be it analog with film or digital
UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 115.3 Physics and the Universe FINAL EXAMINATION December 19, 2015 NAME: (Last) Please Print (Given) Time: 3 hours STUDENT
Ch 8. Rotational Dynamics Rotational W, P, K, & L (a) Translation (b) Combined translation and rotation ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS = τ Iα Requirement:
Clearly communicate your understanding of the physics principles that you are going to solve a question and how those principles apply to the problem at hand. You may communicate this understanding through
Absolute motion versus relative motion in Special Relativity is not dealt with properly Roger J Anderton R.J.Anderton@btinternet.com A great deal has been written about the twin paradox. In this article
Report on the new EFOSC2 VPH grisms Ivo Saviane Lorenzo Monaco v 1.0 March 01, 2008 1 Introduction In January 2008 the ULTRASPEC project delivered two volume-phased holographic grisms (VPHG) to be used
Chapter 9: Rotational Dynamics Tuesday, September 17, 2013 10:00 PM The fundamental idea of Newtonian dynamics is that "things happen for a reason;" to be more specific, there is no need to explain rest
CHARA Technical Report No. 86 1 August 2000 Imaging and Fourier Coverage: Mapping with Depleted Arrays P.G. Tuthill and J.D. Monnier 1. INTRODUCTION In the consideration of the design of a sparse-pupil
Rotational Dynamics, Moment of Inertia and Angular Momentum Now that we have examined rotational kinematics and torque we will look at applying the concepts of angular motion to Newton s first and second
Flips are Fun: A Study in the Conservation of Angular Momentum of a Non-Rigid Human Body Benjamin Jenkins Physics Department, The College of Wooster, Wooster, Ohio 44691, USA May 10, 2018 Abstract In this
FÉDÉRATION INTERNATIONALE DE GYMNASTIQUE Av. de la Gare 12 1003 Lausanne Suisse Tél. (41-32) 494 64 10 Fax (41-32) 494 64 19 e-mail: email@example.com www. fig-gymnastics.com FIG ACADEMY BIOMECHANICS
APPLICATIONS OF BIOMECHANICS CINEMATOGRAPHY TO RESEARCH AND COACHING ASPECTS OF THE POLE VAULT Hans Josef Gros Universitat Stuttgart Stuttgart, Germany Juris Terauds Research Center for Sports Del Mar,
sice02-0206 A consideration on position of center of ground reaction force in upright posture Satoshi Ito ),2) Yoshihisa Saka ) Haruhisa Kawasaki ) firstname.lastname@example.org email@example.com
Kinematics Kinematics theory Kinematics Mechanics Physics Other areas of physics Processing techniques Statics Dynamics Measurement techniques Introduction to 3D kinematics Kinematics Kinetics Kinematics:
Existence is Difference and is expressed and transformed by Information reality is changing by virtuality and at the same time it reveals the latter s existence and role Ioannis Hadjidakis (NARSEP) firstname.lastname@example.org
Bulletin of the Transilvania University of Braşov CIBv 2014 Vol. 7 (56) Special Issue No. 1-2014 STUDY OF EFFECTS OF VIBRATIONS CAUSED BY RAILWAY TRAFFIC TO BUILDINGS R. NERIŞANU 1 D. DRĂGAN 1 M. SUCIU
5. KINEMATICS Suddenly there is no more acceleration and no more pressure on my body. It is like being at the top of a roller coaster and my whole body is in free-fall. Roberta Bondar, Touching the Earth.
Lab 1: Jumping Right In Bio427 Biomechanics The first lecture of the class reviewed basic physical quantities that we will use throughout the course. Distance (position), velocity, acceleration, momentum,
Surveying Prof. Bharat Lohani Indian Institute of Technology, Kanpur (Refer Slide Time: 00:20) Module 5 Lecture 1 Welcome to this another lecture on basic surveying. Today we are going to start a new module.
PS 12A Lab 3: Forces Names: Learning Goals After you finish this lab, you will be able to: 1. Use Logger Pro to analyze video and calculate position, velocity, and acceleration. 2. Measure the normal force
BIOMECHANICAL MOVEMENT CHAPTER 6: Angular motion, projectile motion and fluid mechanics Angular motion Axis A figure 6.1 planes and axes Sagittal Frontal Angular motion is defined as the motion of a body
Classical mechanics: Newton s laws of motion Homework next week will be due on Thursday next week You will soon be receiving student evaluations Occam s razor Given two competing and equally successful
Fall 008 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton -3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 496 501 The 2014 conference of the International Sports Engineering Association Dynamic contribution analysis of
ESPRIT Feature Particle detection and chemical classification Innovation with Integrity EDS Fast and Comprehensive Feature Analysis Based on the speed and accuracy of the QUANTAX EDS system with its powerful
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 147 (016 ) 677 68 11th conference of the International Sports Engineering Association, ISEA 016 The effect of ball spin rate
8/04/0 Lecture PowerPoints 009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student
SECTION TOPIC 2 4 CHAPTER CHAPTER 6 Practice questions - text book pages 96-99 1) Angle in radians is defined as: a. rate of turning. b. arc length subtending the angle divided by radius of the circle.
Inertial and non-inertial frames: with pieces of paper and in an active way Leoš Dvořák Department of Physics Education, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic
Loughborough University Institutional Repository The biomechanics of twisting somersaults. Part III: aerial twist This item was submitted to Loughborough University's Institutional Repository by the/an
Lecture PowerPoints Chapter 7 Physics for Scientists and Engineers, with Modern Physics, 4 th Edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is
Journal of Biomechanics 34 (2001) 449 456 Dependence of release variables in the shot put MontHubbard a, *, Neville J. de Mestre b, John Scott c a Department of Mechanical and Aeronautical Engineering,
Wheel and Axle Author: Joseph Harrison British Middle-East Center for studies & Research email@example.com http:// bmcsr.com Research Ans Aerospace Engineering 1 Expert, Monash University Introduction A solid
Take it Further Demonstration Versus Angular Speed Purpose Show that tangential speed depends on radius. Materials two tennis balls attached to different lengths of string (approx. 1.0 m and 1.5 m) Procedure
1 (a) Define moment of a force. In your answer, you should use appropriate technical terms, spelled correctly....  (b) State the two conditions that apply when an object is in equilibrium. 1.... 2....
Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2 1000 Ljubljana Slovenija http://www3.fgg.uni-lj.si/ Jamova 2 SI 1000
JOURNAL OF MEDICAL INFORMATICS & TECHNOLOGIES Vol. 15/2010, ISSN 1642-6037 Kalman filtration, filter algorithm, accelerometric sensor Grzegorz SAPOTA 1, Anna SAPOTA 1, Zygmunt WRÓBEL 1 THE USE OF KALMAN
The Airborne Gyroscope Chris Hodgson and Paul Hughes Department of Physics and Astronomy The University of Manchester Manchester M13 9PL First Year Laboratory Report Nov 3 Abstract Gyroscopic motion involves
AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able
Biomechanical Modelling of Musculoskeletal Systems Lecture 6 Presented by Phillip Tran AMME4981/9981 Semester 1, 2016 The University of Sydney Slide 1 The Musculoskeletal System The University of Sydney
Available online at wwwsciencedirectcom Procedia Engineering 34 (22 ) 28 223 9 th Conference of the International Sports Engineering Association (ISEA) Multi-body power analysis of kicking motion based
Chapter 6 Circular Motion, Orbits and Gravity Topics: The kinematics of uniform circular motion The dynamics of uniform circular motion Circular orbits of satellites Newton s law of gravity Sample question: