The center of percussion is a point on a body which, when struck with a force, will have
associated with it another point called the center of rotation at which there will be a zero
reaction force. You have probably experienced the result of "missing the center of percussion"
when you hit a baseball or softball with the wrong spot on the bat. The "right
place on the bat" to hit the ball is the center of percussion associated with the point that
your hands grip the bat (the center of rotation). Hitting the ball at other than the center
of percussion results in a stinging force being delivered to your hands. Hit the right spot
and you feel no force (nor pain). The center of percussion is sometimes called the "sweet
spot" on a bat, tennis racquet, or golf club. In the case of our mallet example, a center of
percussion at the head corresponds to a center of rotation near the end of the handle, and
the handle is usually contoured to encourage gripping it there.
The explanation of this phenomenon is quite simple. To make the example two dimensional
and eliminate the effects of friction, consider a hockey stick of mass m lying
on the ice as shown in Figure 1O-3a. Strike it a sharp blow at point P with a force F perpendicular
to the stick axis. The stick will begin to travel across the ice in complex planar
motion, both rotating and translating. Its complex motion at any instant can be considered
as the superposition of two components: pure translation of its center of gravity
G in the direction ofF and pure rotation about that point G. Set up an embedded coordi