A Performance Analysis System for the Sport of Bowling

3.4.3 Finding the Coefficient of Friction
The coefficient of friction can be recovered from the previous calculations. Under the
assumptions, the only active force is the force due to friction acting between the ball and
the lane, and that force acts solely to transfer linear momentum to angular momentum.
Since the changes in angular and linear momentum for each sample are known, the
frictional force required to generate those changes can be found.
For any revolution i, the frictional force F µi acting during i is given by
Fµi = m / 2 · k(ω 2 i - ω 2 i-1 ) / (D i - D i-1 ) = m / 2 · (v 2 i - v 2 i-1 ) / (D i - D i-1 ).
The coefficient of friction µ i between the ball and the lane for revolution i is then
µ i = Fµi / mg, where g is the acceleration due to gravity.
Similarly, the frictional force for any sample j of revolution i can be found from
Fµi,j = m / 2 · k(ω 2 i,j - ω 2 i,j-1 ) / (d i,j - d i,j-1 ) = m / 2 · (v 2 i,j - v 2 i,j-1 ) / (d i,j - d i,j-1 ).
The coefficient of friction µ i,j between the ball and the lane for any sample j of revolution
i is then given by
µ i,j = Fµi,j / mg.
Using this result, there is now enough information to graph the coefficient of friction
between the ball and the lane with respect to the distance from the foul line.
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