By J.R. Calvert
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Extra resources for An Engineering Data Book
Are kinetic, potential and dissipative energy. 3 - - Moments of Inertia Definitions: Moment oflnertia: I xx = Jr dm 2 M r is the perpendicular distance of the element of mass dm from the axis XX; the integral is taken over the whole mass of the body. Radius of gyration k is defined by I= Mk 2, for a specified axis. Parallel axis theorem: Ixx= IGG + My02 M is the mass of the body, y 0 is the perpendicular distance between an axis GG through the centre of mass and another axis XX parallel to GG. IGG is the minimum moment of inertia for all axes in the given direction.
L = 0 and a= 1. z 2 ,P(z) = - - e 2 J2; z Its cumulative distribution function lP(z) = J~ e -t12 dt -oo is the probability that the random variable is observed to have a value s; z (the shaded area shown in the graph ofN(0,1) on page 4-3). l) "'s ~ , where f(x)dx = 1 = tP -00 4-2 l k (x-p) l u Its cumulative distribution F(x) = e -tr 2 dt = cP( x ~11 ) . Tables of rp(z) and 4\z) may be used for f(x) and F(x) by taking X-11 z=--. 3 Experimental Samples x 1, x 2, ••• Xn denote a set of n observations of a random variable having a normal distribution whose mean 11 is unknown.
_Lix;-ml Sample variance: 1-"" (x; -m) 2 s2 =n - 1£... 58 m -,!! "n with n -1 degrees of freedom (tn-1), and the 95% confidence interval for p is obtained from m ± t c j;; and the table. 96 s I is a good approximation to the population mean with a 95% confidence. 4 Combination of Errors If results are normally distributed, the Most Probable Error Sz in the calculated result z = f(x, y, etc) due to independent standard errors Sx, Sy. etc in x, y, etc is given by: 2 (Sz) = (8zox Sx ) + (8zoy Sy ) + ...