Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 17 - Planar Kinetics of a Rigid Body: Force and Acceleration - Section 17.1 - Mass Moment of Inertia - Problems: 2

Answer

$k_{x}=\sqrt{\frac{I_{x}}{m}}=\sqrt{\frac{5.236*10^{13}}{1.57*10^{10}}}=57.7 mm$

Work Step by Step

$dm=\rho \pi y^{2}dx=\rho \pi (50x)dx$ $I_{x}=\int \frac{1}{2}y^{2}dm=\frac{1}{2} \int 50x(\rho \pi (50x)dx)=1250\rho \pi (\frac{1}{3}(200)^{3})$ $m=\int dm=\int \pi \rho(50x)dx=25(200)^2 \pi \rho$ $k_{x}=\sqrt{\frac{I_{x}}{m}}=\sqrt{\frac{5.236*10^{13}}{1.57*10^{10}}}=57.7 mm$
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