Problem 7: Consider looking down from above at a baseball player swinging his bat in a horizontal plane 1n the process of hitting a baseball at point B. The player 1s holding the bat such that the resultant of the force from his hands 1s at point A. Thus, the bat can be modelled as a rigid object rotating about point joint A. The radius of gyration of the bat about its center of mass, G, 1s kg. Recall: 1; = mk? At what distance d should the ball hit the bat so that the normal (upward) force component at the batter's hands 1s 0? Neglect gravity, because it is negligible compared to forces like P and hand reaction force. k&+1g Ans: d = lg Hint: In other words, given the center of mass location l;, given the moment of inertia and mass of the bat, given some angular velocity and angular acceleration of the bat, find the location d where some vertical force P can be applied such that the vertical reaction at the pin joint A is 0. Note: This point B 1s called the Center of Percussion. Because this kind of hit feel effortless to the batter (and avoids a painful sting at the hands). it 1s often called the \"sweet spot\" by athletes in sports like baseball and tennis