Chapter 17 - Engineering Mechanics - Dynamics Chapter 17...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Engineering Mechanics - Dynamics Chapter 17 Problem 17-1 The right circular cone is formed by revolving the shaded area around the x axis. Determine the moment of inertia I x and express the result in terms of the total mass m of the cone. The cone has a constant density U . Solution: m h x U S rx h § © · ¹ 2 ´ µ µ ¶ d 1 3 h U S r 2 U 3 m h S r 2 I x 3 10 m r 2 I x 3 m h S r 2 h x 1 2 S rx h § © · ¹ 2 rx h § © · ¹ 2 ´ µ µ ¶ d Problem 17-2 Determine the moment of inertia of the thin ring about the z axis. The ring has a mass m . Solution: m 2 S T U R ´ µ ¶ d 2 S U R U m 2 S R I z m 2 S R 2 S T R R 2 ´ µ ¶ d m R 2 I z m R 2 Problem 17-3 The solid is formed by revolving the shaded area around the y axis. Determine the radius of gyration k y . The specific weight of the material is J . Given: J 380 lb ft 3 a 3 in b 3 in 504 Engineering Mechanics - Dynamics Chapter 17 Solution: m b y J S a y 3 b 3 § ¨ © · ¸ ¹ 2 ´ µ µ µ ¶ d m 0.083 slug I y b y J 1 2 S a y 3 b 3 § ¨ © · ¸ ¹ 2 a y 3 b 3 § ¨ © · ¸ ¹ 2 ´ µ µ µ ¶ d I y 0.201 slug in 2 ¡ k I y m k 1.56 in *Problem 17-4 Determine the moment of inertia I x of the sphere and express the result in terms of the total mass m of the sphere.The sphere has a constant density U . Solution: m r r x U S r 2 x 2 + , ´ µ ¶ d 4 3 r 3 U S U 3 m 4 S r 3 I x 3 m 4 S r 3 r r x S 2 r 2 x 2 + , 2 ´ µ µ ¶ d I x 2 5 m r 2 Problem 17-5 Determine the radius of gyration k x of the paraboloid. The density of the material is U . Units Used: Mg 10 6 gm Given: h 200 mm r 100 mm U 5 Mg m 3 505 Engineering Mechanics - Dynamics Chapter 17 Solution: M h x U S x r 2 h § ¨ © · ¸ ¹ ´ µ µ ¶ d M 15.708 kg I x h x 1 2 U S x r 2 h § ¨ © · ¸ ¹ 2 ´ µ µ µ ¶ d I x 0.052 kg m 2 ¡ k x I x M k x 57.7 mm Problem 17-6 Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density U . Solution: m a x U S b 2 1 x 2 a 2 § ¨ © · ¸ ¹ ´ µ µ µ ¶ d 2 3 a U S b 2 U 3 m 2 a S b 2 I x 3 m 2 a S b 2 a x 1 2 S b 2 1 x 2 a 2 § ¨ © · ¸ ¹ ª « ¬ º » ¼ 2 ´ µ µ µ ¶ d I x 2 5 m b 2 Problem 17-7 Determine the radius of gyration k x of the body. The specific weight of the material is J . Given: J 380 lb ft 3 h 8 in r 2 in 506 Engineering Mechanics - Dynamics Chapter 17 Solution: M h x J S r x h § © · ¹ 1 3 ª « « ¬ º » » ¼ 2 ´ µ µ µ µ ¶ d M 0.412 slug I x h x 1 2 J S r x h § © · ¹ 1 3 ª « « ¬ º » » ¼ 4 ´ µ µ µ µ ¶ d I x 0.589 slug in 2 ¡ k x I x M k x 1.20 in *Problem 17-8 Determine the moment of inertia of the ellipsoid with respect to the x axis and express the result in terms of the mass m of the ellipsoid. The material has a constant density U ....
View Full Document

This note was uploaded on 04/13/2008 for the course ME 2580 taught by Professor Vandenbrink during the Spring '08 term at Western Michigan.

Page1 / 87

Chapter 17 - Engineering Mechanics - Dynamics Chapter 17...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online