10 Solutions 44918 1/28/09 4:21 PM Page 927 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–1 Determine the moment of inertia of the area about the x axis y 2m y ϭ 0.25 x3 x 2m 927 10 Solutions 44918 1/28/09 4:21 PM Page 928 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–2 Determine the moment of inertia of the area about the y axis y 2m y ϭ 0.25 x3 x 2m 928 10 Solutions 44918 1/28/09 4:21 PM Page 929 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–3 Determine the moment of inertia of the area about the x axis y 1m y2 ϭ x3 x 1m 929 10 Solutions 44918 1/28/09 4:21 PM Page 930 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *10–4 Determine the moment of inertia of the area about the y axis y 1m y2 ϭ x3 x 1m 930 10 Solutions 44918 1/28/09 4:21 PM Page 931 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–5 Determine the moment of inertia of the area about the x axis y y2 ϭ 2x 2m x 2m 931 10 Solutions 44918 1/28/09 4:21 PM Page 932 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–6 Determine the moment of inertia of the area about the y axis y y2 ϭ 2x 2m x 2m 932 10 Solutions 44918 1/28/09 4:21 PM Page 933 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–7 Determine the moment of inertia of the area about the x axis y y ϭ 2x4 2m O 933 x 1m 10 Solutions 44918 1/28/09 4:21 PM Page 934 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *10–8 Determine the moment of inertia of the area about the y axis y y ϭ 2x4 2m O 934 x 1m 10 Solutions 44918 1/28/09 4:21 PM Page 935 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–9 Determine the polar moment of inertia of the area about the z axis passing through point O y y ϭ 2x4 2m O 935 x 1m 10 Solutions 44918 1/28/09 4:21 PM Page 936 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–10 Determine the moment of inertia of the area about the x axis y y ϭ x3 in x in 10–11 Determine the moment of inertia of the area about the y axis y y ϭ x3 in x in 936 10 Solutions 44918 1/28/09 4:22 PM Page 1019 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z *10–104 The thin plate has a mass per unit area of 10 kg>m2 Determine its mass moment of inertia about the z axis 200 mm 200 mm 100 mm 200 mm 100 mm 200 mm 200 mm x 1019 200 mm 200 mm 200 mm y 10 Solutions 44918 1/28/09 4:22 PM Page 1020 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–105 The pendulum consists of the 3-kg slender rod and the 5-kg thin plate Determine the location y of the center of mass G of the pendulum; then find the mass moment of inertia of the pendulum about an axis perpendicular to the page and passing through G O y 2m G 0.5 m 1m 1020 10 Solutions 44918 1/28/09 4:22 PM Page 1021 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z 10–106 The cone and cylinder assembly is made of homogeneous material having a density of 7.85 Mg>m3 Determine its mass moment of inertia about the z axis 150 mm 300 mm 150 mm 300 mm x 1021 y 10 Solutions 44918 1/28/09 4:22 PM Page 1022 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–107 Determine the mass moment of inertia of the overhung crank about the x axis The material is steel having a density of r = 7.85 Mg>m3 20 mm 30 mm 90 mm 50 mm x 180 mm 20 mm x¿ 30 mm 20 mm 1022 50 mm 30 mm 10 Solutions 44918 1/28/09 4:22 PM Page 1023 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *10–108 Determine the mass moment of inertia of the overhung crank about the x¿ axis The material is steel having a density of r = 7.85 Mg>m3 20 mm 30 mm 90 mm 50 mm x 180 mm 20 mm x¿ 30 mm 20 mm 1023 50 mm 30 mm 10 Solutions 44918 1/28/09 4:22 PM Page 1024 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–109 If the large ring, small ring and each of the spokes weigh 100 lb, 15 lb, and 20 lb, respectively, determine the mass moment of inertia of the wheel about an axis perpendicular to the page and passing through point A ft ft O A 1024 10 Solutions 44918 1/28/09 4:22 PM Page 1025 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–110 Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O The material has a mass per unit area of 20 kg>m2 O 50 mm 150 mm 50 mm 400 mm 400 mm 150 mm 150 mm 1025 150 mm 10 Solutions 44918 1/28/09 4:22 PM Page 1026 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–111 Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O The material has a mass per unit area of 20 kg>m2 O 200 mm 200 mm 200 mm 1026 10 Solutions 44918 1/28/09 4:22 PM Page 1027 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *10–112 Determine the moment of inertia of the beam’s cross-sectional area about the x axis which passes through the centroid C y d d 60Њ x C 60Њ d •10–113 Determine the moment of inertia of the beam’s cross-sectional area about the y axis which passes through the centroid C d y d d 60Њ d 1027 x C 60Њ d 10 Solutions 44918 1/28/09 4:22 PM Page 1028 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–114 Determine the moment of inertia of the beam’s cross-sectional area about the x axis y yϭ a a –x –– a x a 1028 a 10 Solutions 44918 1/28/09 4:22 PM Page 1029 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–115 Determine the moment of inertia of the beam’s cross-sectional area with respect to the x¿ axis passing through the centroid C in 0.5 in _ y 2.5 in C x¿ 0.5 in 0.5 in *10–116 Determine the product of inertia for the angle’s cross-sectional area with respect to the x¿ and y¿ axes having their origin located at the centroid C Assume all corners to be right angles y¿ 57.37 mm 20 mm 200 mm C 20 mm 200 mm 1029 x¿ 57.37 mm 10 Solutions 44918 1/28/09 4:22 PM Page 1030 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–117 Determine the moment of inertia of the area about the y axis y 4y ϭ – x ft x ft 10–118 Determine the moment of inertia of the area about the x axis y 4y ϭ – x ft x ft 1030 10 Solutions 44918 1/28/09 4:22 PM Page 1031 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 10–119 Determine the moment of inertia of the area about the x axis Then, using the parallel-axis theorem, find the moment of inertia about the x¿ axis that passes through the centroid C of the area y = 120 mm y 200 mm 200 mm C –y x¿ y ϭ ––– x2 200 x 1031 10 Solutions 44918 1/28/09 4:22 PM Page 1032 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *10–120 The pendulum consists of the slender rod OA, which has a mass per unit length of kg>m The thin disk has a mass per unit area of 12 kg>m2 Determine the distance y to the center of mass G of the pendulum; then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G O y 1.5 m G A 0.1 m 0.3 m 1032 10 Solutions 44918 1/28/09 4:22 PM Page 1033 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •10–121 Determine the product of inertia of the area with respect to the x and y axes y 1m y ϭ x3 x 1m 1033 ... publisher *10 32 Determine the moment of inertia of the composite area about the x axis y 150 mm 150 mm 100 mm 100 mm x 300 mm 951 75 mm 10 Solutions 44918 1/28/09 4:22 PM Page 952 © 2 010 Pearson... publisher 10 33 Determine the moment of inertia of the composite area about the y axis y 150 mm 150 mm 100 mm 100 mm x 300 mm 952 75 mm 10 Solutions 44918 1/28/09 4:22 PM Page 953 © 2 010 Pearson... from the publisher 10 31 Determine the moment of inertia of the beam’s cross-sectional area about the y axis y 60 mm 15 mm 60 mm 15 mm 100 mm 15 mm 50 mm x 50 mm 100 mm 15 mm 950 10 Solutions 44918