Linear and angular kinetics
3.5 Spatial rotation
Summary 119 axis is displaced away from its original position of coincidence with the
angular momentum vector (sometimes called the axis of momentum), and will describe a cone around that vector.
Furthermore, the equation of conservation of angular momentum (Equation 3.24) applies to an inertial frame of reference, such as one moving with the centre of mass of the performer but always parallel to a fixed, stationary frame of reference. The conservation of angular momentum does not generally apply to a frame of reference fixed in the performer’s body and rotating with it. For a further discussion of some aspects of spatial rotation, see Yeadon (1993).
In this chapter linear kinetics were considered, which are important for an understanding of human movement in sport and exercise. This included the definition of force and its SI unit, the identification of the various external forces acting in sport, the laws of linear kinetics and related concepts such as linear momentum, and the ways in which force systems can be classified.
The segmentation method for calculating the position of the whole body centre of mass of the sports performer was explained. Some important forces were considered in more detail. The ways in which friction and traction influence movements in sport and exercise were addressed, including reducing and increasing friction and traction. An appreciation was provided of the factors that govern impact, both direct and oblique, of sports objects, and the centre of percussion was introduced and related to sports objects and performers. The vitally important topic of rotational kinetics was covered, including the laws of rotational kinetics and related concepts such as angular momentum and the ways in which rotation is acquired and controlled in sports motions. The chapter concluded with a very brief introduction to spatial (three-dimensional) rotation.
Figure 3.24 Nutation.
3.6 Summary
1. Define force in terms of its SI unit. List the external forces that act on the sports performer and, for each force, give an example of a sport or exer-cise in which that force will be very important. Draw sketches of ex-amples from sport and exercise of each of the force system classifications in section 3.1.2.
2. Define and explain the three laws of linear kinetics and give at least two examples from sport or exercise, other than the examples in this chapter, of the application of each law.
3. Photocopy Figure 3.6, or trace on to graph paper the outline of the thrower.
Use the x,y axes and the segment end points of Figure 3.6. Measure the x and y coordinates of each of the segment end points. Then use a photo-copy of Table 3.1 to calculate the position of the thrower’s whole body centre of mass in the units of the image. Finally, as a check on your calculation, mark the resulting centre of mass position on your figure. If it looks silly, check your calculations and repeat until the centre of mass position appears reasonable.
4. Carry out the inclined plane experiment of section 3.2.1 to calculate the coefficient of friction between the plane’s surface and training shoes and other sports objects. (You only need a board of material, a shoe and a protractor.)
5. List some examples, other than those of section 3.2, of sports in which methods are used to increase and decrease friction to aid performance.
6. Using the equations for the critical angular velocity and critical approach angle in section 3.3, establish for the following examples, in all of which e=0.7, whether the solid ball will slide throughout impact or roll. Where appropriate, establish any other facts you can about the ball’s behaviour after impact from the information in section 3.3.
a) Ball radius 35 mm, µ=0.5, v=20 m·s-1,α=80°, ω=0.
b) Ball radius 35 mm, µ=0.5, v=20 m·s-1, α=30°, ω=-200 rad·s-1. c) Ball radius 70 mm, µ=0.6, v=5 m·s-1, α=30°, ω=800 rad·s-1.
7. Distinguish between moments of inertia and products of inertia. Define, and explain, the three laws of angular kinetics and give at least two ex-amples from sport or exercise of the application of each law.
8. Consider the ways in which angular momentum can be generated (sec-tion 3.4.5). Give examples of each from sport and exercise movements.
9. Obtain a video recording of top class diving, trampolining or gymnastics.
Carefully analyse some airborne movements that do not involve twisting, including the transfer of angular momentum between body segments.
10. Repeat Exercise 9 for movements involving twisting. Consider in particu-lar the ways in which the performers generate twist in somersaulting move-ments.
3.7 Exercises
Table 3.1 Calculation of the two-dimensional whole body centre of mass position (data from Dempster (1955), adjusted to correct for fluid loss)
Table 3.2 Radii of gyration for body segments (values calculated from the data of Chandler et al
Bell, M.J., Baker, S.W. and Canaway, P.M. (1985) Playing quality of sport surfaces: a review. Journal of the Sports Turf Research Institute, 61, 30–38.
Chandler, R.F., Clauser, C.E., McConville, J.T. et al. (1975) Investigation of inertial properties of the human body. Report DOT HS-801 430, US Department of Transportation, Washington, DC.
Clauser, C.E., McConville, J.T. and Young, J.W. (1969) Weight, volume and center of mass of segments of the human body. Report AMRL-TR-69–70, Wright-Patterson Air Force Base, Aerospace Medical Research Laboratory, Dayton, OH.
Coulton, J. (1977) Women’s Gymnastics, EP, Wakefield.
Cureton, T.K. (1951) Physical Fitness of Champion Athletes, University of Illinois Press, Urbana, IL.
Daish, C.B. (1972) The Physics of Ball Games, EUP, Cambridge.
Dempster, W.T. (1955) Space requirements for the seated operator. WADC Technical Report 55159, Wright-Patterson Air Force Base, Wright Air Development Centre, Dayton, OH.
Hay, J.G. (1993) The Biomechanics of Sports Techniques, Prentice Hall, Englewood Cliffs, NJ.
Malina, R.M. (1969) Growth and physical performance of African negro and white children. Clinical Pediatrics, 8, 476–483.
Page, R.L. (1978) The Physics of Human Movement, Wheaton, Exeter.
Payne, H. (ed.) (1985) Athletes in Action, Pelham Books, London.
Stucke, H., Baudzus, W. and Baumann, W. (1984) On friction characteristics of playing surfaces, in Sports Shoes and Playing Surfaces, (ed. E.C.Frederick), Human Kinetics, Champaign, IL, pp.87–97.
Thomas, D.G. (1989) Swimming: Steps to Success, Leisure Press, Champaign, IL.
Yeadon, M.R. (1993) The biomechanics of twisting somersaults. Journal of Sports Sciences, 11, 187–225.
Daish, C.B. (1972) The Physics of Ball Games, EUP, Cambridge: chapters 2 and 3 present a non-mathematical treatment of impact. The mathematically inclined reader will also benefit from reading chapters 10 and 15.
Page, R.L. (1978) The Physics of Human Movement, Wheaton, Exeter: chapter 3 deals with centre of mass measurement.
Stucke, H., Baudzus, W. and Baumann, W. (1984) On friction characteristics of playing surfaces, in Sports Shoes and Playing Surfaces, (ed. E.C.Frederick), Human Kinetics, Champaign, IL: pp.87–97.
3.8 References
3.9 Further reading