partial answer(b) u = p*w^2*x/6*E (3*L^2-x^2)(c) small sigma max = 3308 psiumax = 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 isgiven 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 andthe 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.Xdx

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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

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

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

partial answer

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

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

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