Center of Percussion
center of percussion - center of oscillation - sweet spot - center of gravity - torque
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.
Comments:
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. Rating **
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.