8 ROTATIONAL MOTION 8.10 The physics of baseball
pivotJ’ J’bat
b
centre of mass
h
l v
ballJ JFigure 82: A schematic baseball bat.The existence of a “sweet spot” on a baseball bat is just a consequence of ro-tational dynamics. Let us analyze this problem. Consider the schematic baseball
bat shown in Fig. 82. Let M be the mass of the bat, and let l be its length. Sup-
pose that the bat pivots about a fixed point located at one of its ends. Let the
centre of mass of the bat be located a distance b from the pivot point. Finally,
suppose that the ball strikes the bat a distance h from the pivot point.
The collision between the bat and the ball can be modeled as equal and oppo-site impulses, J, applied to each object at the time of the collision (see Sect. 6.5).
At the same time, equal and opposite impulses JJ are applied to the pivot and the
bat, as shown in Fig. 82. If the pivot actually corresponds to a hitter’s hands then
the latter impulse gives rise to the painful jarring sensation felt when the ball is
not struck properly.
We saw earlier that in a general multi-component system—which includes anextended body such as a baseball bat—the motion of the centre of mass takes
a particularly simple form (see Sect. 6.3). To be more exact, the motion of the
centre of mass is equivalent to that of the point particle obtained by concentrating
the whole mass of the system at the centre of mass, and then allowing all of the
external forces acting on the system to act upon that mass. Let us use this idea to