### Demos: 1Q-08 Center of Percussion

If an impulsive force is applied at an arbitrary point on a suspended object, there will, in general, be a reaction force at the suspension point. If the distance from the suspension point to the point of impact is chosen carefully, no such reaction force will occur. This point of impact is called the center of percussion.

The demonstration consists of a suspended baseball bat and a baseball that is allowed to swing through an arc and strike the bat at different points. When the center of percussion is struck, the suspension point shows no reaction force. At other points the reaction force is evident from the rapid movement at the suspension.

Analysis shows that the distance for the center of percussion is

where I0 is the moment of inertia about the axis and d is the distance to the center of mass. If the bat were a uniform cylinder of length L, then the center of percussion would be located at 2/3 L.

Directions: The bat will be set up by the lecture-demo staff. In performing the demo, stand behind the swinging ball so you can be sure of aligning the arc of swing so the ball hits the bat. Begin by choosing lengths of the cord will cause the bat to strike above and below the center of percussion.

Suggestions for Presentation: Ask the students if they have heard the term "sweet spot" as it relates to sports. You will likely get answers that relate to such a point on baseball bats, tennis racquets, etc. Then ask how you know when the ball has hit this spot as opposed to some other spot. (For a baseball bat, the reaction force at the handle causes what is referred to as a "sting.") Show the origin of the "sting" by allowing the ball to hit the bat at some point other than the center of percussion. Point out the visible reaction at the suspension point. Then let it hit the sweet spot and show that the reaction is minimal. Use this to discuss how you know when you've hit the sweet spot.

Applications: Sports equipment such as baseball bats, tennis racquets, etc.

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Last Updated: May 9, 2016 11:44 AM