partial answer (b) u = p*w^2*x/6*E (3*L^2-x^2) (c) small sigma max = 3308 psi umax = 2.28(10^-3)in

Elements Of Electromagnetics
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partial answer

(b) u = p*w^2*x/6*E (3*L^2-x^2)

(c) small sigma max = 3308 psi

umax = 2.28(10^-3)in

A steel rod of length L rotates with a constant angular velocity w in a horizon-
tal plane about the y axis.
(a) Prove that the internal axial stress in the rod due to dynamic effects is
given by pw² (L² - x²)/2, where p is the mass density of the rod.
(b) From part (a) determine the deflection of the rod as a function of x and
the variables p, w, E, and L.
(c) Plot the results of parts (a) and (b) if the weight density of steel y =
0.284 lb/in³, L = 30 in, E = 29 Mpsi, and w = 100 rad/s.
X
dx
Transcribed Image Text:A steel rod of length L rotates with a constant angular velocity w in a horizon- tal plane about the y axis. (a) Prove that the internal axial stress in the rod due to dynamic effects is given by pw² (L² - x²)/2, where p is the mass density of the rod. (b) From part (a) determine the deflection of the rod as a function of x and the variables p, w, E, and L. (c) Plot the results of parts (a) and (b) if the weight density of steel y = 0.284 lb/in³, L = 30 in, E = 29 Mpsi, and w = 100 rad/s. X dx
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