O' is the center of oscillation for point O, and vice versa . This condition gives the minimum period of oscillation T min for a given rigid body. In this case, the axis or rotation is not fixed but moves at constant velocity . This general case is analyzed on pages 322 - 326. Instead of considering forces, the above results can be obtained from conservation of energy .
P is the impulse delivered from the ball to the bat.
The conclusion is the same if the bat is swung and the ball is stationary, or if both have motion prior to the collision. If the door is swung, a doorstop placed at the center of percussion will result in all the angular momentum being absorbed by the stop and no force on the hinges.