Problem

A batter is swinging a 34 in. long bat with weight WB= 32 oz, mass center G, and mass mome...

A batter is swinging a 34 in. long bat with weight WB= 32 oz, mass center G, and mass moment of inertia IG = 0.0413 slug·ft2. The center of rotation of the bat is point Q. Compute the distance d identifying the position of point P, the bat’s “sweet spot” or center of percussion, such that the batter will not feel any impulsive forces at O where he is grasping the bat. In addition, knowing that the ball, weighing 5 oz, is traveling at a speed υb = 90 mph and that the batter is swinging the bat with an angular velocity ω0 = 45 rad/s, determine the speed of the ball and the angular velocity of the bat immediately after impact. To solve the problem, use the following data: δ = 6 in., ρ = 14 in., ℓ = 22.5 in., and COR e = 0.5.