# Force of a Windmill Slam Dunk: Dominique Wilkins

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## Abstract

The purpose of this analysis is to find the centripetal force Dominique exerts on the basketball in one of his "windmill" slam dunks.

## Introduction

Dominique Wilkins a NBA basketball player a.k.a "Human Highlight Film" earned his nickname due to his acrobatic skills. His basketball career dated back to his college years in Georgia. He is a giant of a man being 6'8" and was named to seven NBA teams. He is also a two-time winner of the NBA slam dunk contest and is one of only twelve basketball players to ever score more than 25,000 points in their entire career.

In the 1988 All-star dunk contest between Dominique Wilkins and Michael Jordan, he performed a windmill dunk being recorded as "One of America's Top Ten Dunks in History". In this analysis we will find the centripetal force Dominique exerts on the ball in the slam dunk by using the formulas

F = ma_{c}

"F" is the total force necessary for the dunk, it is equal to the "m" (mass of basketball) multiplied by the "a" (centripetal acceleration of the motion. To find the centripetal acceleration
which is equal to "r" (radius) multiplied by ω^{2} (rotational velocity squared):

a_{c} = rω^{2}

We will be analyzing his dunk from a video source using frame by frame to measure his velocity.

## Analysis

The video "Michael Jordan vs Dominique Wilkins for Dunk Title" is available at YouTube.

According to internet sources [here] Dominique Wilkins is 6' 8" (2.03 m). I scaled the length of his arm using a ruler (on my computer screen) and compared it to the known length of the diameter of a basketball to find the length of his arm; in this case it is the "radius" of the formula

a_{c} = rω^{2}

His arm (r) is approximately 2' 7" (0.78 m).

To determine the angular speed of his dunk, I used QuickTime video player and measured the frame rate. The frame rate of QuickTime is 29.97 FPS. It took 15 frames for him to "Windmill Dunk", therefore the time it takes is 0.5 seconds.

To find his angular speed, I used the equation:

angular speed = (change in angle)/time

ω = 2π/0.5 s

ω = 12.6 radians/seconds

To find the centripetal acceleration, I used the formula:

centripetal acceleration = (angular speed)^{2} x radius

a_{c} = (12.6 rad/sec)^{2} x (0.7874 s)

a_{c} = 124 m/s^{2}

Finally, to find the centripetal force of the dunk, I used the formula:

F_{c} = ma_{c}

Plugging in the mass of the basketball 0.62 kg [here] into the formula,

F_{c} = (0.62 kg) x (124 m/s^{2})

F_{c} = 76.88 N

## Conclusion

From the measurements above we have estimated the force Dominique used in his "windmill" Dunks to be 76.88 N. The amount of force necessary to "dunk" a basketball is considered low when compared to the amount of force used in other sports, such as in golf and baseball, stretching from 2000 N to over 10,000 N [here].

## Sources of Error

In this analysis there are many factors that serve as sources of error to the calculated results. These sources of error include the estimated measurements of "r" the radius which is the length of Dominique's arm. Since the length of his arms are unknown, to estimate his arm length I had to compare the known length of the basketball's diameter to the length of his arms. Anther source of error is that Dominique's Dunk is not a perfect "loop", and since the formula used to measure his centripetal acceleration is made to measure objects traveling in perfect circles, it will contribute to a wrong calculation of the acceleration.

Zhao Liang -- 2005

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