Introduction to Sports Biomechanics: Analysing Human Movement ...

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CAUSES OF MOVEMENT – FORCES AND TORQUES Figure 5.17 Generation of rotation: (a) an eccentric force; (b) addition of two equal and opposite collinear forces acting through the centre of mass, G; (c) equivalence to a ‘pure’ force and a torque; (d) checking of linear motion. This, as shown in Figure 5.17(d), is merely a special case of an eccentric force. It is best considered in that way to avoid misunderstandings that exist in the literature, such as the misconception that O is the instantaneous centre of rotation. This last sentence begs the question of where the instantaneous centre of rotation does lie in such cases. Consider a rigid body that is simultaneously rotating with angular velocity ω about its centre of mass while moving linearly, as in Figure 5.18(a). The whole body has the same linear velocity (v), as in Figure 5.18(b), but the tangential velocity owing to rotation (v t) depends on the displacement (r) from the centre of mass, G, such that v t = ω × r, as in Figure 5.18(c). Adding v and v t gives the net linear velocity (Figure 5.18(d)) that, at some point P (which need not lie within the body) is zero; this point is called the instantaneous centre of rotation and its position usually changes with time. Consider now a similar rigid body acted upon by an impact force, as in Figure 5.18(e), which is similar to Figure 5.17(d). There will, in general, be a point R that will experience no net acceleration. By Newton’s second law of linear motion, the magnitude of the acceleration of the centre of mass of the rigid body, mass m, is a g = F/m. From Newton’s second law of rotation (see above), the magnitude (F c) of the moment of the force F is equal to the product of the moment of inertia of the body about its centre of mass (I g) and its angular acceleration (α). That is F c = I g α. This gives a tangential acceleration (α r) that increases linearly with distance (r) from G. The 197
INTRODUCTION TO SPORTS BIOMECHANICS Figure 5.18 Instantaneous centre of rotation and centre of percussion: (a) rigid body undergoing linear and angular motion; (b) linear velocity profile; (c) tangential velocity profile; (d) net velocity profile and instantaneous centre of rotation (P); (e) impact force on a rigid body at centre of percussion (Q); (f) net acceleration profile. 198 net acceleration profile then appears as in Figure 5.18(f). At point R (r = b), the two accelerations are equal and opposite and, therefore, cancel to give a zero net acceleration. The position of R is given by equating F/m (= a g) to F b c/I g, the tangential acceleration at R. That is: b c = I g/m. If R is a fixed centre of rotation then Q is known as the centre of percussion, defined as that point at which a force may be applied without
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Introduction to Sports Biomechanics
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First edition published 1997 This e
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Contents List of figures x List of
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Study tasks 216 Glossary of importa
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FIGURES 1.26 Underarm throw - femal
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FIGURES 5.9 Typical path of a swimm
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Tables 2.1 Examples of slowest sati
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Preface Why have I changed the cove
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Introduction MISSING TEXT The first
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INTRODUCTION principal movements in
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INTRODUCTION TO SPORTS BIOMECHANICS
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Figure 2.2 ‘Principles’ approac
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Figure 2.13 Identifying critical fe
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INDEX 282 balls air flow past 173 b
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INDEX 284 energy 219 kinetic 219 mi
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INDEX 286 isokinetic contraction 24
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INDEX 288 muscle length-tension rel
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INDEX 290 three-dimensional 146-7,
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INDEX 292 validity 220 vantage poin
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