# Force of a Windmill Slam Dunk: Vince Carter

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## Abstract

The purpose of this analysis is to determine the centripetal force on a basketball after Vince Carter has performed a 360 degree windmill dunk.

## Introduction

Vince, aka "Vinsanity" and "Air Canada", is arguably the best dunker in NBA history, out-dunking the greats Dominique Wilkins, Michael Jordan and the Doctor J himself. This man is said to have a no conscience when on the basketball court. As soon as he drives the lane, he elevates and posterizes all who stand his way. According to thefreedictionary.com posterize is "North American slang derived from an action in the game of basketball, in which the offensive player dunks over a defending player in a play that is spectacular and athletic enough to warrant reproduction in a printed poster. The term is also derisive in that when a defending player is "posterized" -- he or she is considered to have been humbled, shamed, and exposed as less athletic. One of the best-known examples of a player being posterized is found in the 2000 Summer Olympics where Vince Carter, playing for the United States' olympic basketball team, dunked over 7' 2" Frederic Weis of France during a game. In the 2000 NBA slam dunk contest, Vince Carter, formerly of the Toronto Raptors, performed a dunk which according to NBA TV was the fifth best dunk in slam dunk history. He started from about the three point line and as soon as he got close enough to the rim he elevated, rotated 360 degrees and turned his hand three-quarters of a circle. I am going to determine the centripetal force on the basketball by his right arm during the dunk using the formula

F_{c} = mv^{2}/r

Where m is mass of the ball, and r is the length of his right arm.

## Procedure

- Find a video containing the Vince Carter dunk.
- Watch the dunk and pause it the instant he gets ready to move his right arm.
- Using Quicktime video player to figure out to figure out the time it takes for Carter to go three-quarters of a circle. When you reach the point at which Carter starts the circle, pause the video and look at the time. When Carter finishes the dunk, pause the video and look at the time. The difference in time is the time it took him to complete the circle.
- Calculate the length of Carter's arm using an arm-length ratio. Set up the ratio by saying my arm length is to arm length as my height is to his height.
- Find the velocity of his arms.
- Find the centripetal acceleration.
- Calculate Fc using the previous values.

## Analysis

The mass of a basketball is 0.624 kg. That is the given. Next we must find the length of his arm using a ratio. The length of my arm is 0.8 meters, and I am 1.85 m tall. Vince Carter is 1.98 m tall. We use a ratio and say

0.8 m : 1.85 m = x : 1.98 m

x = (0.8 m)(1.98 m)/(1.85 m)

x = 0.86 m

The instant when Carter's arm begins to revolve is 4.09 seconds. The instant when he reaches the end of the circle is 4.23 seconds. Therefore the time it took for him to go three-quarters of a circle was 0.14 seconds. Now we can find the velocity of his arms using the formula

v = 2π r/t

But since it wasn't a full circle we multiply by 0.75

v = (0.75)(2π)(0.86 m)/(0.14 s)

v = 28.94 m/s

Now that we know the velocity, v, we can find the centripetal acceleration and ultimately the centripetal force.

a_{c} = v^{2}/r

a_{c} = (28.94 m/s)^{2}/(0.86 m)

a_{c} = 974 m/s^{2}

F_{c} = ma_{c}

F_{c} = (0.624 kg)(974 m/s^{2})

F_{c} = 607 N

## Conclusion

The centripetal force on the basketball by Vince Carter right hand is 607 N.

## Sources of Error

- One source of error is that Vince's arm may didn't exactly move in three-quarters of a circle. It is a close approximation.
- The second possible error is that not all people's body parts are in the same proportion. Vince's arm may be longer or shorter than mine in proportion to his height.

Oluwemimo Oladapo -- 2005

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