Example 2: Calculate the mass of the uniform disc when its moment of inertia is 110 kg m2 and its radius is 10 m. what Im unsure of is how to relate that x distance into the moment of inertia formula so that I can know what each body is contributing to the whole. We have for solid sphere, MOI (I) 2/5 MR 2. Therefor, I know all the centers of mass are y 0, and I can calculate all the x distances (dx in my drawing). The results suggest that, with Japanese boys, there is a relationship between the postures and body size (height or weight), independent of age. Example 1: Determine the solid sphere’s moment of inertia at a mass of 22 kg and a radius of 5 m. When Imx and Imy were estimated using these equations, the standard deviation of error which calculates the percent differences between the estimated and measured values amounted to +/- 5% in Imx and Imy. This law is analogous to linear momentum being conserved when the external force on a system is zero. Any of the individual angular momenta can change as long as their sum remains constant. The multiple regression analysis of Ht2 and W with regard to Im was performed to obtain the following multiple regression equations: Imx = 3.44 Ht2 + 0.144 W - 8.04 (R = 0.973), Imy = 3.52 Ht2 + 0.125 W - 7.78 (R = 0.972). 11.11 Note that the total angular momentum L is conserved. The difference between Imx and Imy might be affected by projection areas on the frontal from the sagittal area of the body. The moment of inertia I of the whole body about DE is the summation of the above expression. The values of Imy/Imx becomes 93.6 and 95.2% independent of age and body size. The moment of inertia of the point mass about the axis DE is, m ( x + d) 2. Both Imx and Imy account for the range from 5.6 to 14.0 kg m2 and 4.2 to 13.5 kg m2, respectively, and correlate linearly to body height (Ht) and body weight (W). Moment of inertia was measured in two postures of supine (Imx) and recumbent (Imy) positions. ![]() One hundred and seventeen subjects of junior and senior high school boys of ages 13-18 participated in this study. Now, we can write the equation for the moment of inertia as. ![]() This study measured the moment of inertia of the body using the oscillating table method, and saw how it is affected by age and body size. A is the surface area of the sphere which is 4R2, and we can write da to be equal to the area of the thin disk we considered, and it will be 2 × Rsin × Rd.
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