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Sports Science Laboratory Bat-Ball Science Mass Moment of Inertia

## Mass Moment of Inertia

The mass moment of inertia (MOI) is a measure of the distribution of mass in the bat. A knob and end loaded bat may weigh the same, for instance, but the end loaded bat will have a higher MOI. Bat speed depends on MOI, and is an important component of laboratory performance tests.

Another (and important) mass property of a bat is denoted the mass moment of inertia (or MOI). It describes the distribution of the mass of a bat. Consider, for instance, a knob and end loaded bat of the same total mass. The end loaded bat will feel heavier when rotated about its pivot point or when swung. As with the COP, the MOI is found from its average period, t, obtained while swinging freely about a pivot point 6 inches from the knob, as

where is the total weight of the bat (ounces), is again the acceleration of gravity (386 in/s2) and BP  is the balance point described above, measured with respect to the knob. The units of MOI are unusual (oz in2), and are indicative of its description of the distribution of mass. The MOI described above is taken about a location 6 inches from the knob [d]. The MOI of 34 inch slow pitch bats will typically range between 7,000 and 10,000 oz in2. Fast pitch bats are usually lighter and shorter which lowers their MOI, in some cases approaching 5,000 oz in2. Baseball bats tend to have an MOI between 8,000 and 10,000 oz in2.

[d] Sometimes MOI is reported with respect to the knob. Thus when comparing bat MOI, it is important to note the reference location. Bat MOI can change dramatically with the reference location due to its dependence on distance squared. Bat MOI at the knob, for instance, will be approximately 50% larger than the MOI 6 inches from the knob.

A note on mass. Weight is measured in units of force (lbs) and will depend on gravity. For measurements taken on the earth’s surface, even with large changes in elevation, gravity is relatively constant. Mass is weight divided by the acceleration of gravity (386 in/s2). Mass is independent of gravity making it a convenient term for intergalactic travel and other uses. Thus, the weight and mass of an object are different numerically, but describe the same entity that must be hefted. Since bat MOI is usually reported in ounces (which is a force) a more correct term would be to call it the weight moment of inertia. Convention indicates otherwise, however, so the casual practitioner should we wary of units and convert from weight to mass when necessary.