Chapter 10, Problem 90GP

Center of Percussion In the previous problem, suppose a small metal ball of mass m = 2M is attached to the rod a distance d from the pivot. The rod and ball are released from rest in the horizontal position. (a) Show that when the rod reaches the vertical position, the speed of its tip is

$v_t=\sqrt{3gL}\sqrt{\frac{1+4(d/L)}{1+6{(d/L)}^2}}$

(b) At what finite value of d/L is the speed of the rod the same as it is for d = 0? (This value of d/L is the center of percussion, or “sweet spot,” of the rod.)