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The centre of percussionCOP is not a unique point on1 M5 n, Q3 q- w
the barrel since it is defined in terms of a conjugate point in4 V- @( Z( [" G% y8 R
2,6,7# v1 F) d; H" j0 ~4 x% S
the handle. Each point in the handle is associated with a* {9 i ?# m* ^3 }( [. _
different COP in the barrel. When a ball strikes a freely* h, t2 Z! C' E
suspended bat, the bat will translate in the direction of the
" B& J6 a! \0 S' T3 K1 Rincident ball and it will also rotate about the centre of mass.) x8 Q# j9 g9 L; \( z( E5 i3 v y
The combined effects of translation and rotation result in a
2 E! B! P. a t- i% nshift of the actual axis of rotation, away from the centre of
- T' ^5 h* z, Amass toward the handle. The axis passes through the conju-
* B0 m' T2 {8 E5 A# ~/ cgate point for that particular impact. If b is the distance from, B8 I+ ?" @5 b( L9 G; t; ?
the impact point to the centre of mass, and x is the distance
! g$ |$ y! y" {8 {8 m: vfrom the centre of mass to the conjugate point, then xIcm/(Mb) where Icm is the moment of inertiaof the bat
9 [2 i8 _- @$ G1 J ]$ j. babout its centre of mass and M is the mass of the bat. Con-! Z. l9 j( Y3 G, G/ c \9 E
sequently, if the bat is pivoted about an axis through the
9 q3 Z+ @5 N0 ?conjugate point, and if the ball strikes the corresponding
! R4 E3 W! ~: U5 ?6 y7 d) V+ rCOP, then there is no reaction force at the pivot point. It is0 w! G+ k( f- k- N
therefore reasonable to expect that every point under the* p4 l& C0 M( I) U1 G3 k. }) C
hands will have its own COP and that an impact at any given
1 P2 P7 m$ H) a& ~+ UCOP will generate zero reaction force at the corresponding. k5 m7 c6 E; E, A, f
8, ~# {" y2 a' Y3 h Z
conjugate point under the hands. Brancazio has suggested+ K: H5 L) p4 o1 n
that the sweet spot zone might therefore encompass all cor-9 S* a$ Y, \' u
responding COP points along the barrel. There is, however,# W! Y. F9 y6 S" |( Y; w2 ?
an uncertainty in this argument since a hand-held bat is not; Q& O8 ?/ h e1 `% p! F {
freely suspended, nor is it pivoted about a single axis, and
% A- {) W- ]8 M1 smay behave differently as a result of the reaction forces ex-3 Y* Z! \5 q" t% {4 g8 {
erted by the two hands. Furthermore, the axis of rotation may( y; O f6 l$ t1 ?2 a8 l1 Z
even shift as a function of time since the ball remains in: t/ |% _3 {1 N- d @5 O- @# F
contact with the bat for about 1.5 ms, the transmission time
4 Y8 E G/ d, K; X1 {, b) O) Oof the pulse from the impact point to the hands is about 1 ms, f Q: G" t5 {; r1 U
and the impact forces on the hands last for about 20 ms as a2 x, l( `9 x D# {5 v* B
result of the induced vibrations and the induced motion of9 F- p& E" m6 _
the bat. |
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