When defining the COR we need to ignore this rapid variation in speed caused by vibration of the bat

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When measuring the bounce off a bat it is usually more convenient to clamp the handle in a vice or to pivot the bat about an axis through the handle, as described in Project 9 and in Chap. 10 (Sect. 10.8). In fact, most bats are tested these days by firing a ball at high speed onto the barrel of a http://www.fifa15sale.com bat that is initially at rest and free to rotate about an axis through the handle. In the latter case, we define the COR in exactly the same way as that for a completely free bat. That is, the COR is the relative speed of the bat and ball after the collision, divided by the incoming ball speed, the bat speed after the collision being the speed of the impact point (as indicated in Fig. 8.7).

In the case of a bat with a clamped handle, the velocity of the bat after the col- lision is zero, so the COR is just the speed of the ball after the collision divided by the speed of the ball before the collision. The bat will vibrate strongly after the collision, but the vibration speed is not counted when we measure the recoil speed of the bat. The bat doesn’t recoil at all.

Even if the bat is freely suspended or pivots around an axis, it will still vi-brate unless it is struck at the sweet spot. Suppose that a given point on the bat rotates through a distance of 1 in. in 0.01 s. The speed of the bat at that point is then 100 in. s-1 . However, if the bat is also vibrating, the surface of the bat can simulta-neously move back and forth by say 0.1 in. in 0.01 s, or at a speed of 10 in. s-1 in one direction and then 10 in. s-1 in the other direction. The actual speed of the bat at that point can therefore vary rapidly between 90 and 110 in. s-1 . When defining the COR we need to ignore this rapid variation in speed caused by vibration of the bat, and just take the average speed, which in this case would be 100 in. s-1. Energy given to the bat in the form of bat vibrations is eventually lost in the bat and in the player’s arms, and is not part of the overall kinetic energy retained by the bat and the ball. Rather, it is part of the energy that is lost.