## Derivation of the Shoulder Pull Formula

Shoulder Pull is the centripetal force, in Newtons,with the shoulder being a distance `R` (= 0.61 + `r`/100) meters from the racquet mass center. The Shoulder Pull force, measured in units of Newtons (1 Newton = 0.225 lb.) attributable to the racquet alone is derived from the Work formula and the general formula for centripetal force (centrifugal force). See the accompanying remarks. A complete description of all variables used in this derivation follows at the end.

Legend of Variables`I` | = | moment of inertia (swing weight) of racquet, in kilograms·centimeters² |
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`b` | = | mass of ball, in kilograms |
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`d` | = | distance from axis of rotation to impact point, in centimeters |
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`s` | = | ball velocity, in meters-per-second (positive is away from player) |
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`r` | = | distance from axis of rotation to mass center, in centimeters |
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`v` | = | linear velocity of mass center, in meters-per-second |
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`M` | = | mass of racquet, in kilograms |
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`c` | = | coefficient of restitution of the racquet/ball system |
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