The motion (or lack of motion) of the suspension point of an object is observed when the object is struck a blow.
What it shows
The center of percussion (COP) is the place on a bat or racket where it may be struck without causing reaction at the point of support. When a ball is hit at this spot, the contact feels good and the ball seems to spring away with its greatest speed and therefore this is often referred to as the sweet spot. At points other than this spot, the bat or racket may vibrate or even sting your hands. This experiment shows the effect by demonstrating what happens when you strike a suspended model of a bat at various places.
How it works
When a bat or racket is struck at its center of gravity (COG), it moves forward (without rotation) in the direction of the force. Hitting a bat or racket at some place other than its COG produces a torque about its COG resulting in both rotational as well as translational motion, as illustrated below for the case of a stick.
Furthermore, there is a point which, when struck, will result in the forward translational velocity and the backward rotational velocity being equal and opposite. This point is called the center of percussion.
2 × 4 stud (140 cm long) represents our bat and is suspended from a horizontal stud by a U-bolt (fixed to one end of the 2 × 4 ) as shown above. The 2 × 4 can rotate about the point of suspension and the suspension U-bolt (pivot point) can itself move horizontally.
In the first of the three situations depicted in the drawings, a force (hammer blow) is applied below the COP. This results in a considerable rotational counterclockwise velocity (greater than the forward translational velocity) and the suspension point gets jerked to the left. If the force is applied between the COP and the COG (middle illustration), the forward velocity will exceed the rotational velocity at the pivot point and there will be a forward push on the pivot point to the right. Hitting above the COG (not illustrated) will impart rotational and translational velocities in the same direction, and the suspension point will clearly move to the right. In the third instance, the 2 × 4 is struck at the COP, which is located 2/3 the way down. The forward and rotational velocities are equal and opposite at the suspension point, which remains stationary.
Sometimes the center of percussion is referred to as the center of oscillation. The reason for this can be demonstrated by suspending a simple pendulum whose length is equal to the distance from the pivot point to the COP. The 2 × 4 and the pendulum will have the same period of oscillation. 1
Setting it up
This is easy—just support the horizontal suspension stud from a couple of lab clamps attached to the lecture bench. The horizontal stud has a shallow V-notch cut into it for the suspension bolt to rest in. The bolt jumps out of the notch when a point other than the COP is hit. A hard rubber mallet or hammer completes the setup. We have a selection of real baseball bats and tennis rackets if the lecturer wishes to go that route.
It might be fun to try real baseball bats and tennis rackets. These could be suspended and hit at various points. Because their shapes are more complex, it will take a little experimenting to identify the COP location. Timing the period of oscillation and computing the corresponding simple pendulum length should do the trick. Comparing the locations of the COP of wooden and aluminum bats could also be instructive.
1 The 2 × 4 is a physical pendulum whose period of oscillation is , compared to a simple pendulum whose period is . Thus a simple pendulum 2/3 the length of a physical pendulum will have an identical period.