Center of percussion

The center of percussion is the point on an extended massive object attached to a pivot where a perpendicular impact will produce no reactive shock at the pivot.

Translational and rotational motions cancel at the pivot when an impulsive blow is struck at the center of percussion.

The center of percussion is often discussed in the context of a bat, racquet, door, sword or other extended object held at one end.

Only if the blow falls exactly on the CP will the two components of motion cancel out to produce zero net initial movement at point P. When the sliding fixture is replaced with a pivot that cannot move left or right, an impulsive blow anywhere but at the CP results in an initial reactive force at the pivot.

is applied at right angle at a point of impact, defined as a distance

Moreover, the force produces a torque about the CM, which results in the change in angular velocity

[1] For the special case of a beam of uniform density of length

, the moment of inertia around the CM is: and for rotation about a pivot at the end, This leads to: It follows that the CP is 2/3 of the length of the uniform beam

The sweet spot on a baseball bat is generally defined as the point at which the impact feels best to the batter.

The center of percussion defines a place where, if the bat strikes the ball and the batter's hands are at the pivot point, the batter feels no sudden reactive force.

However, since a bat is not a rigid object the vibrations produced by the impact also play a role.

Research has shown that the dominant physical mechanism in determining where the sweet spot is arises from the location of nodes in the vibrational modes of the bat, not the location of the center of percussion.

Being flexible objects, the "sweet spot" for such cutting weapons depends not only on the center of percussion but also on the flexing and vibrational characteristics.