According to the standard practice used by manufacturers, test labs and governing bodies, the pivot point is taken to be on the handle 6-inches from the knob end of the bat.
The moment-of-inertia is always calculated or measured with respect to a specified pivot point.
Knowing the location of the balance point is important. The weight of the bat is just the sum of the two scale readings W = W 6 + W 24 and the balance point is calculated from BP = (6*W 6 + 24*W 24) / (W 6 + W 24) This test standard requires the use of two scales, one which supports the bat at a point 6-inches from the end of the knob, and the other which supports the barrel of the bat at a distance of 24-inches from the knob. Or you could follow the procedure for measuring weight and balance point as spelled out in ASTM Standard F2398-04 "Test Method for Measuring Moment of Inertia and Center of Percussion of a Baseball of Softball Bat" which is what bat manufacturers and governing associations do. This is a bit tricky but it works pretty well. To find the balance point, you could use a knife edge and find the location where the bat exactly balances. To measure the weight of the bat you could just put it on a scale and record the weight directly. It turns out that the moment-of-inertia is much easier to measure than it is to calculate, so I won't attempt to explain how we would solve for the inertia, but instead will describe how it is measured and what it means.Įxtended object (bat) pivoting about a fixed axis may be broken up into many small pieces with varying mass and varying distance from the pivot point.
However, very few people actually have the mass distribution function dm for a given baseball or softball bat at their fingertips, so calculating the moment-of-inertia for a bat isn't very practical. If we knew how the mass dm varied with position we could add all the individual moments-of-inertia together to obtain the total inertia of the bat. In order to solve this more difficult problem, we pretend that the bat is made up of very large number of very small slices, each with its own incremental mass dm and each being located at a distance x from the pivot point. In our case the object which is rotating is a bat, with mass distributed along its entire length. Multiple point masses rotating at a various distances from a pivot point. If there are several point objects all rotating about the same pivot point, but at different distances from the pivot, then the total moment-of-inertia of the system is just the sum of the individual moments-of-inertia. Single point mass rotating at a fixed distance from a pivot point. The MOI of the point mass is the product of the mass and the square of the distance from the pivot point: The value of the MOI depends on the total mass of the object as well as the way in which that mass is distributed about the pivot point.Ĭonsider first a point mass m (a small ball) which is rotating parallel to the ground at a distance x from a fixed pivot point, as is shown in the image at top right. The larger the moment-of-inertia, the more difficult it is to change the rotational speed of the object. Rotational inertia, or the moment-of-inertia (MOI) is a measure of how difficult it is to change the rotational velocity of an object which is rotating about a pivot point. Mass is different from weight though the two terms are often used interchangeably. The greater the inertia of an object ( i.e., the more mass an object has), the more difficult it is to change its velocity. Moment-of-Inertia of a Baseball or Softball Bat Inertia is a measure of how difficult it is to change the velocity of an object by applying a force, and is usually expressed in terms of mass. Today is The contents of this page were last modified on September 4, 2008 The contents of this page are ©2008 Daniel A.
Physics and Acoustics of Baseball & Softball BatsĪpplied Physics, Kettering University, Flint, MI 48504-4898