Problem

Following up on the center of percussion mini-example on p. 552, now assume that the pivot...

Following up on the center of percussion mini-example on p. 552, now assume that the pivot point O is close to the center of mass of the batter so that it is a distance δ = 3 in. from the knob of the bat at A. Determine the location of the center of percussion P relative to the knob at A and show that the position of P is independent of the location of point C at which the batter grips the bat. Recall that P is the point at which the ball should be hit so that, no matter how large the force applied at P to the bat by the ball, the lateral force (i.e., perpendicular to the bat) felt by the batter at the grip C is zero. Assume the bat has mass m, its mass center is at G, and IG is its mass moment of inertia. Evaluate your answer for a typical bat used in Major League Baseball whose weight is 32 oz and whose length is 34 in., ℓ = 22.5 in., m = 0.0630 slug, and IG = 0.0413 slug · ft2. Ignore the weight force on the bat.