Moment of Inertia and Centroid
|
|
- Alexandrina Bates
- 6 years ago
- Views:
Transcription
1 Chapter- Moment of nertia and Centroid Page- 1. Moment of nertia and Centroid Theory at a Glance (for ES, GATE, PSU).1 Centre of gravity: The centre of gravity of a body defined as the point through which the whole weight of a body may be assumed to act.. Centroid or Centre of area: The centroid or centre of area is defined as the point where the whole area of the figure is assumed to be concentrated.. Moment of nertia (MO) About any point the product of the force and the perpendicular distance between them is known as moment of a force or first moment of force. This first moment is again multiplied by the perpendicular distance between them to obtain second moment of force. n the same way if we consider the area of the figure it is called second moment of area or area moment of inertia and if we consider the mass of a body it is called second moment of mass or mass moment of nertia. Mass moment of inertia is the measure of resistance of the body to rotation and forms the basis of dynamics of rigid bodies. Area moment of nertia is the measure of resistance to bending and forms the basis of strength of materials.. Mass moment of nertia (MO) mr i i i Notice that the moment of inertia depends on the distribution of mass in the system. The further the mass is from the rotation axis, the bigger the moment of inertia. For a given object, the moment of inertia depends on where we choose the rotation axis.
2 Chapter- Moment of nertia and Centroid Page- n rotational dynamics, the moment of inertia appears in the same way that mass m does in linear dynamics. Solid disk or cylinder of mass M and radius R, about perpendicular axis through its centre, 1 MR Solid sphere of mass M and radius R, about an axis through its centre, /5 M R Thin rod of mass M and length L, about a perpendicular axis through its centre. 1 1 ML Thin rod of mass M and length L, about a perpendicular axis through its end. 1 ML.5 Area Moment of nertia (MO) or Second moment of area To find the centroid of an area by the first moment of the area about an axis was determined ( x da ) ntegral of the second moment of area is called moment of inertia ( x da) Consider the area ( A ) By definition, the moment of inertia of the differential area about the x and y axes are d and d d y da y da d x da x da
3 Chapter- Moment of nertia and Centroid Page-.6 Parallel axis theorem for an area: The rotational inertia about any axis is the sum of second moment of inertia about a parallel axis through the C.G and total area of the body times square of the distance between the axes. NN CG + Ah.7 Perpendicular axis theorem for an area: f x, y & z are mutually perpendicular axes as shown, then zz ( J) + Z-axis is perpendicular to the plane of x-y and vertical to this page as shown in figure. To find the moment of inertia of the differential area about the pole (point of origin) or z- axis, (r) is used. (r) is the perpendicular distance from the pole to da for the entire area J r da (x + y )da + (since r x + y ) Where, J polar moment of inertia.8 Moments of nertia (area) of some common area: (i) MO of Rectangular area Moment of inertia about axis XX which passes through centroid. Take an element of width dy at a distance y from XX axis. Area of the element (da) b dy. and Moment of nertia of the element about XX axis da y b.y.dy Total MO about XX axis (Note it is area moment of nertia) + h h bh by dy by dy 1 h 0
4 Chapter- Moment of nertia and Centroid Page- Similarly, we may find, hb 1 Polar moment of inertia (J) + bh hb bh 1 f we want to know the MO about an axis NN passing through the bottom edge or top edge. Axis XX and NN are parallel and at a distance h/. Therefore NN + Area (distance) bh h bh + b h 1 Case-: Square area a 1 Case-: Square area with diagonal as axis a 1
5 Chapter- Moment of nertia and Centroid Page- 5 Case-: Rectangular area with a centrally rectangular hole Moment of inertia of the area moment of inertia of BG rectangle moment of inertia of SMALL rectangle BH bh 1 1.(ii) MO of a Circular area The moment of inertia about axis XX this passes through the centroid. t is very easy to find polar moment of inertia about point O. Take an element of width dr at a distance r from centre. Therefore, the moment of inertia of this element about polar axis d(j) d( + ) area of ring or d(j) π rdr r (radius) ntegrating both side we get R πr πd J π r dr 0 Due to summetry Therefore, 6 J πd πd πd and J 6
6 Chapter- Moment of nertia and Centroid Page- 6 Case : Moment of inertia of a circular area with a concentric hole. Moment of inertia of the area moment of inertia of BG circle moment of inertia of SMALL circle. πd - π d 6 6 π 6 π (D d ) and J (D d ) Case : Moment of inertia of a semi-circular area. 1 NN of the momemt of total circular lamina 1 πd πd 6 18 We know that distance of CG from base is r D hsay ( ) π π i.e. distance of parallel axis XX and NN is (h) According to parallel axis theory NN ( ) + Area distance G πd 1 πd or + ( h) 18 πd 1 πd D or + 18 π or 0.11R
7 Chapter- Moment of nertia and Centroid Page- 7 Case : Quarter circle area XX one half of the moment of nertia of the Semicircular area about XX. 1 XX ( 0.11R ) R XX 0.055R NN one half of the moment of nertia of the Semicircular area about NN. 1 πd πd NN 6 18 (iii) Moment of nertia of a Triangular area (a) Moment of nertia of a Triangular area of a axis XX parallel to base and passes through C.G. XX bh 6 (b) Moment of inertia of a triangle about an axis passes through base NN bh 1
8 Chapter- Moment of nertia and Centroid Page- 8 (iv) Moment of inertia of a thin circular ring Polar moment of nertia ( ) J R area of whole ring R πrt πr t J XX YY πr t (v) Moment of inertia of a elliptical area XX πab Let us take an example: An -section beam of 100 mm wide, 150 mm depth flange and web of thickness 0 mm is used in a structure of length 5 m. Determine the Moment of nertia (of area) of cross-section of the beam. Answer: Carefully observe the figure below. t has sections with symmetry about the neutral axis.
9 Chapter- Moment of nertia and Centroid Page- 9 We may use standard value for a rectangle about an axis passes through centroid. i.e. bh. The section can 1 thus be divided into convenient rectangles for each of which the neutral axis passes the centroid. - Beam Rectangle Shaded area ( ) m m.9 Radius of gyration: Consider area A with moment of inertia. magine that the area is concentrated in a thin strip parallel to the x axis with equivalent. k A or k A k radius of gyration with respect to the x axis. Similarly k A or k A J ko A or ko k k + k o J A Let us take an example: Find radius of gyration for a circular area of diameter d about central axis. Answer:
10 Chapter- Moment of nertia and Centroid Page- 10 We know that, K A or K π d 6 d A πd XX XX
11
ME 201 Engineering Mechanics: Statics
ME 0 Engineering Mechanics: Statics Unit 9. Moments of nertia Definition of Moments of nertia for Areas Parallel-Axis Theorem for an Area Radius of Gyration of an Area Moments of nertia for Composite Areas
More informationSub:Strength of Material (22306)
Sub:Strength of Material (22306) UNIT 1. Moment of Inertia 1.1 Concept of Moment of Inertia (Ml). Effect of MI in case of beam and column. 1.2 MI about axes passing through centroid. Parallel and Perpendicular
More informationChapter 6: Cross-Sectional Properties of Structural Members
Chapter 6: Cross-Sectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross
More informationSecond Moments or Moments of Inertia
Second Moments or Moments of Inertia The second moment of inertia of an element of area such as da in Figure 1 with respect to any axis is defined as the product of the area of the element and the square
More informationProperties of surfaces II: Second moment of area
Properties of surfaces II: Second moment of area Just as we have discussing first moment of an area and its relation with problems in mechanics, we will now describe second moment and product of area of
More informationMOI (SEM. II) EXAMINATION.
Problems Based On Centroid And MOI (SEM. II) EXAMINATION. 2006-07 1- Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R. 2- State the parallel axis theorem.
More informationHong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 2 SECTION PROPERTIES
Section Properties Centroid The centroid of an area is the point about which the area could be balanced if it was supported from that point. The word is derived from the word center, and it can be though
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 17
ENGR-1100 Introduction to Engineering Analysis Lecture 17 CENTROID OF COMPOSITE AREAS Today s Objective : Students will: a) Understand the concept of centroid. b) Be able to determine the location of the
More information10.5 MOMENT OF INERTIA FOR A COMPOSITE AREA
10.5 MOMENT OF NERTA FOR A COMPOSTE AREA A composite area is made by adding or subtracting a series of simple shaped areas like rectangles, triangles, and circles. For example, the area on the left can
More informationStatics: Lecture Notes for Sections 10.1,10.2,10.3 1
Chapter 10 MOMENTS of INERTIA for AREAS, RADIUS OF GYRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the MoI for an area by integration.
More informationChapter 10: Moments of Inertia
Chapter 10: Moments of Inertia Chapter Objectives To develop a method for determining the moment of inertia and product of inertia for an area with respect to given x- and y-axes. To develop a method for
More informationENGI Multiple Integration Page 8-01
ENGI 345 8. Multiple Integration Page 8-01 8. Multiple Integration This chapter provides only a very brief introduction to the major topic of multiple integration. Uses of multiple integration include
More informationProperties of Sections
ARCH 314 Structures I Test Primer Questions Dr.-Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body
More informationMAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPPALLI Distinguish between centroid and centre of gravity. (AU DEC 09,DEC 12)
MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPPALLI 621213 Sub Code: GE 6253 Semester: II Subject: ENGINEERING MECHANICS Unit III: PROPERTIES OF SURFACES AND SOLIDS PART A 1. Distinguish between centroid and
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any cross-section of a beam may consists of a resultant normal force,
More informationCentroid & Moment of Inertia
UNIT Learning Objectives Centroid & Moment of Inertia After studying this unit, the student will be able to Know what is centre of gravity and centroid Calculate centroid of geometric sections Centre of
More informationMoments of Inertia. Notation:
RCH 1 Note Set 9. S015abn Moments of nertia Notation: b d d d h c Jo O = name for area = name for a (base) width = calculus smbol for differentiation = name for a difference = name for a depth = difference
More informationStatics: Lecture Notes for Sections
0.5 MOMENT OF INERTIA FOR A COMPOSITE AREA A composite area is made by adding or subtracting a series of simple shaped areas like rectangles, triangles, and circles. For example, the area on the left can
More informationAREAS, RADIUS OF GYRATION
Chapter 10 MOMENTS of INERTIA for AREAS, RADIUS OF GYRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the MoI for an area by integration.
More informationREVOLVED CIRCLE SECTIONS. Triangle revolved about its Centroid
REVOLVED CIRCLE SECTIONS Triangle revolved about its Centroid Box-in Method Circle Sector Method Integrating to solve I, Ax, and A for a revolved triangle is difficult. A quadrilateral and another triangle
More informationMoments of Inertia (7 pages; 23/3/18)
Moments of Inertia (7 pages; 3/3/8) () Suppose that an object rotates about a fixed axis AB with angular velocity θ. Considering the object to be made up of particles, suppose that particle i (with mass
More informationTwo small balls, each of mass m, with perpendicular bisector of the line joining the two balls as the axis of rotation:
PHYSCS LOCUS 17 summation in mi ri becomes an integration. We imagine the body to be subdivided into infinitesimal elements, each of mass dm, as shown in figure 7.17. Let r be the distance from such an
More informationENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01
ENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01 3. Multiple Integration This chapter provides only a very brief introduction to the major topic of multiple integration. Uses of multiple
More informationDistributed Forces: Moments of Inertia
Distributed Forces: Moments of nertia Contents ntroduction Moments of nertia of an Area Moments of nertia of an Area b ntegration Polar Moments of nertia Radius of Gration of an Area Sample Problems Parallel
More informationSemester: BE 3 rd Subject :Mechanics of Solids ( ) Year: Faculty: Mr. Rohan S. Kariya. Tutorial 1
Semester: BE 3 rd Subject :Mechanics of Solids (2130003) Year: 2018-19 Faculty: Mr. Rohan S. Kariya Class: MA Tutorial 1 1 Define force and explain different type of force system with figures. 2 Explain
More information2015 ENGINEERING MECHANICS
Set No - 1 I B. Tech I Semester Supplementary Examinations Aug. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More informationME 141. Lecture 8: Moment of Inertia
ME 4 Engineering Mechanics Lecture 8: Moment of nertia Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil679@gmail.com Website: teacher.buet.ac.bd/sshakil
More information2. Supports which resist forces in two directions. Fig Hinge. Rough Surface. Fig Rocker. Roller. Frictionless Surface
4. Structural Equilibrium 4.1 ntroduction n statics, it becomes convenient to ignore the small deformation and displacement. We pretend that the materials used are rigid, having the propert or infinite
More informationPHYS 211 Lecture 21 - Moments of inertia 21-1
PHYS 211 Lecture 21 - Moments of inertia 21-1 Lecture 21 - Moments of inertia Text: similar to Fowles and Cassiday, Chap. 8 As discussed previously, the moment of inertia I f a single mass m executing
More informationh p://edugen.wileyplus.com/edugen/courses/crs1404/pc/b03/c2hlch...
n this appendix we discuss... 1 of 4 16-Sep-12 19:35 APPENDIX C In this appendix we discuss how to calculate the moment of inertia of an area. 1 The moment of inertia of an area was first introduced in
More informationSTATICS. Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Ninth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
N E 9 Distributed CHAPTER VECTOR MECHANCS FOR ENGNEERS: STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Teas Tech Universit Forces: Moments of nertia Contents ntroduction
More information15.3. Moment of inertia. Introduction. Prerequisites. Learning Outcomes
Moment of inertia 15.3 Introduction In this section we show how integration is used to calculate moments of inertia. These are essential for an understanding of the dynamics of rotating bodies such as
More information14.1. Multiple Integration. Iterated Integrals and Area in the Plane. Iterated Integrals. Iterated Integrals. MAC2313 Calculus III - Chapter 14
14 Multiple Integration 14.1 Iterated Integrals and Area in the Plane Objectives Evaluate an iterated integral. Use an iterated integral to find the area of a plane region. Copyright Cengage Learning.
More informationMOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION
MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine
More informationSet No - 1 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS
3 Set No - 1 I B. Tech I Semester Regular Examinations Jan./Feb. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Question Paper Consists
More informationSTATICS. Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Seventh Edition CHAPTER. Ferdinand P. Beer
00 The McGraw-Hill Companies, nc. All rights reserved. Seventh E CHAPTER VECTOR MECHANCS FOR ENGNEERS: 9 STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Distributed Forces: Lecture Notes: J. Walt Oler
More informationUSHA RAMA COLLEGE OF ENGINEERING & TECHNOLOGY
Set No - 1 I B. Tech II Semester Supplementary Examinations Feb. - 2015 ENGINEERING MECHANICS (Common to ECE, EEE, EIE, Bio-Tech, E Com.E, Agri. E) Time: 3 hours Max. Marks: 70 Question Paper Consists
More informationMTE 119 STATICS FINAL HELP SESSION REVIEW PROBLEMS PAGE 1 9 NAME & ID DATE. Example Problem P.1
MTE STATICS Example Problem P. Beer & Johnston, 004 by Mc Graw-Hill Companies, Inc. The structure shown consists of a beam of rectangular cross section (4in width, 8in height. (a Draw the shear and bending
More informationENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AND STRUCTURAL ENGINEERING C105 TUTORIAL 1 - MOMENTS OF AREA
ENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AN STRUCTURAL ENGINEERING C105 TUTORIAL 1 - MOMENTS OF AREA The concept of first and second moments of area is fundamental to several areas of engineering
More informationMoment of inertia. Contents. 1 Introduction and simple cases. January 15, Introduction. 1.2 Examples
Moment of inertia January 15, 016 A systematic account is given of the concept and the properties of the moment of inertia. Contents 1 Introduction and simple cases 1 1.1 Introduction.............. 1 1.
More informationME 101: Engineering Mechanics
ME 0: Engineering Mechanics Rajib Kumar Bhattacharja Department of Civil Engineering ndian nstitute of Technolog Guwahati M Block : Room No 005 : Tel: 8 www.iitg.ernet.in/rkbc Area Moments of nertia Parallel
More informationBASIC MATHS TUTORIAL 7 - MOMENTS OF AREA. This tutorial should be skipped if you are already familiar with the topic.
BASIC MATHS TUTORIAL 7 - MOMENTS OF AREA This tutorial should be skipped if you are already familiar with the topic. In this section you will do the following. Define the centre of area. Define and calculate
More information2015 ENGINEERING MECHANICS
Set No - 1 I B.Tech I Semester Regular/Supple. Examinations Nov./Dec. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem. E, Aero E, AME, Min E, PE, Metal E, Textile Engg.) Time: 3 hours
More informationDEFINITION OF MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA
DEFINITION OF MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the moment of inertia
More informationHandout 6: Rotational motion and moment of inertia. Angular velocity and angular acceleration
1 Handout 6: Rotational motion and moment of inertia Angular velocity and angular acceleration In Figure 1, a particle b is rotating about an axis along a circular path with radius r. The radius sweeps
More informationChapter 9 Moment of Inertia
Chapter 9 Moment of Inertia Dr. Khairul Salleh Basaruddin Applied Mechanics Division School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) khsalleh@unimap.edu.my PARALLEL-AXIS THEOREM,
More informationCOURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More informationSTATICS. Distributed Forces: Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
007 The McGraw-Hill Companies, nc. All rights reserved. Eighth E CHAPTER 9 VECTOR MECHANCS FOR ENGNEERS: STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University
More informationMechanics of Structure
S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI
More informationPESIT- Bangalore South Campus Dept of science & Humanities Sub: Elements Of Civil Engineering & Engineering Mechanics 1 st module QB
PESIT- Bangalore South Campus Dept of science & Humanities Sub: Elements Of Civil Engineering & Engineering Mechanics 1 st module QB Sub Code: 15CIV13/23 1. Briefly give the scope of different fields in
More informationJNTU World. Subject Code: R13110/R13 '' '' '' ''' '
Set No - 1 I B. Tech I Semester Supplementary Examinations Sept. - 2014 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More informationProperties of plane surfaces I: First moment and centroid of area
Properties of plane surfaces I: First moment and centroid of area Having deal with trusses and frictional forces, we now change gears and go on to discuss some properties of surfaces mathematically. Of
More informationJNTU World. Subject Code: R13110/R13
Set No - 1 I B. Tech I Semester Regular Examinations Feb./Mar. - 2014 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More informationStrength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee
Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Lecture - 28 Hi, this is Dr. S. P. Harsha from Mechanical and
More informationPART-A. a. 60 N b. -60 N. c. 30 N d. 120 N. b. How you can get direction of Resultant R when number of forces acting on a particle in plane.
V.S.. ENGINEERING OLLEGE, KRUR EPRTMENT OF MEHNIL ENGINEERING EMI YER: 2009-2010 (EVEN SEMESTER) ENGINEERING MEHNIS (MEH II SEM) QUESTION NK UNIT I PRT- EM QUESTION NK 1. efine Mechanics 2. What is meant
More informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
More informationChapter 5. Distributed Forces: Centroids and Centers of Gravity
Chapter 5 Distributed Forces: Centroids and Centers of Gravity Application There are many examples in engineering analysis of distributed loads. It is convenient in some cases to represent such loads as
More informationENGINEERING MECHANICS
Set No - 1 I B. Tech II Semester Regular/Supply Examinations July/Aug. - 2015 ENGINEERING MECHANICS (Common to ECE, EEE, EIE, Bio-Tech, E Com.E, Agri. E) Time: 3 hours Max. Marks: 70 Question Paper Consists
More informationSub. Code:
Important Instructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may
More information[8] Bending and Shear Loading of Beams
[8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight
More informationwhere G is called the universal gravitational constant.
UNIT-I BASICS & STATICS OF PARTICLES 1. What are the different laws of mechanics? First law: A body does not change its state of motion unless acted upon by a force or Every object in a state of uniform
More informationArnie Pizer Rochester Problem Library Fall 2005 WeBWorK assignment VMultIntegrals1Double due 04/03/2008 at 02:00am EST.
WeBWorK assignment VMultIntegralsouble due 04/03/2008 at 02:00am ST.. ( pt) rochesterlibrary/setvmultintegralsouble/ur vc 8.pg Consider the solid that lies above the square = [0,2] [0,2] and below the
More information1.1. Rotational Kinematics Description Of Motion Of A Rotating Body
PHY 19- PHYSICS III 1. Moment Of Inertia 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body 1.1.1. Linear Kinematics Consider the case of linear kinematics; it concerns the description
More informationTOPIC D: ROTATION EXAMPLES SPRING 2018
TOPIC D: ROTATION EXAMPLES SPRING 018 Q1. A car accelerates uniformly from rest to 80 km hr 1 in 6 s. The wheels have a radius of 30 cm. What is the angular acceleration of the wheels? Q. The University
More informationFurther Linear Elasticity
Torsion of cylindrical bodies Further Linear Elasticity Problem Sheet # 1. Consider a cylindrical body of length L, the ends of which are subjected to distributions of tractions that are statically equivalent
More information14. Rotational Kinematics and Moment of Inertia
14. Rotational Kinematics and Moment of nertia A) Overview n this unit we will introduce rotational motion. n particular, we will introduce the angular kinematic variables that are used to describe the
More informationEngineering Tripos Part IIA Supervisor Version. Module 3D4 Structural Analysis and Stability Handout 1
Engineering Tripos Part A Supervisor Version Module 3D4 Structural Analysis and Stability Handout 1 Elastic Analysis (8 Lectures) Fehmi Cirak (fc86@) Stability (8 Lectures) Allan McRobie (fam @eng) January
More informationMOMENT OF INERTIA. Applications. Parallel-Axis Theorem
MOMENT OF INERTIA Today s Objectives: Students will be able to: 1. Determine the mass moment of inertia of a rigid body or a system of rigid bodies. In-Class Activities: Applications Mass Moment of Inertia
More informationSOLUTION Determine the moment of inertia for the shaded area about the x axis. I x = y 2 da = 2 y 2 (xdy) = 2 y y dy
5. Determine the moment of inertia for the shaded area about the ais. 4 4m 4 4 I = da = (d) 4 = 4 - d I = B (5 + (4)() + 8(4) ) (4 - ) 3-5 4 R m m I = 39. m 4 6. Determine the moment of inertia for the
More informationAnna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions.
Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions 1. Find the resultant force and its direction for the given figure 2. Two forces are acting at a point O as shown in
More informationMoment Of Inertia Solutions Meriam File Type
We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with moment of inertia solutions
More informationCIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:
MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationSTATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.
STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle
More informationAdvanced Structural Analysis EGF Section Properties and Bending
Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear
More informationBending Stress. Sign convention. Centroid of an area
Bending Stress Sign convention The positive shear force and bending moments are as shown in the figure. Centroid of an area Figure 40: Sign convention followed. If the area can be divided into n parts
More informationUniform Circular Motion:-Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant.
Circular Motion:- Uniform Circular Motion:-Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant. Angular Displacement:- Scalar form:-?s = r?θ Vector
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM - 613 403 - THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
More informationTechnique 1: Volumes by Slicing
Finding Volumes of Solids We have used integrals to find the areas of regions under curves; it may not seem obvious at first, but we can actually use similar methods to find volumes of certain types of
More informationLecture 6: Distributed Forces Part 2 Second Moment of Area
Lecture 6: Distributed Forces Part Second Moment of rea The second moment of area is also sometimes called the. This quantit takes the form of The phsical representation of the above integral can be described
More informationBE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)
BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)
More informationChapter Rotational Motion
26 Chapter Rotational Motion 1. Initial angular velocity of a circular disc of mass M is ω 1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc.
More information(Refer Slide Time: 2:08 min)
Applied Mechanics Prof. R. K. Mittal Department of Applied Mechanics Indian Institute of Technology, Delhi Lecture No. 11 Properties of Surfaces (Contd.) Today we will take up lecture eleven which is a
More informationEngineering Science OUTCOME 1 - TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1 - TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationEngineering Mechanics Questions for Online Examination (Unit-I)
Engineering Mechanics Questions for Online Examination (Unit-I) [1] If two equal forces are acting at a right angle, having resultant force of (20)½,then find out magnitude of each force.( Ans. (10)½)
More informationSample Question Paper
Scheme I Sample Question Paper Program Name : Mechanical Engineering Program Group Program Code : AE/ME/PG/PT/FG Semester : Third Course Title : Strength of Materials Marks : 70 Time: 3 Hrs. Instructions:
More information8 Geometrical properties of cross-sections
8 Geometrical properties of cross-sections 8.1 Introduction The strength of a component of a structure is dependent on the geometrical properties of its crosssection in addition to its material and other
More informationSTATICS Chapter 1 Introductory Concepts
Contents Preface to Adapted Edition... (v) Preface to Third Edition... (vii) List of Symbols and Abbreviations... (xi) PART - I STATICS Chapter 1 Introductory Concepts 1-1 Scope of Mechanics... 1 1-2 Preview
More informationLab #4 - Gyroscopic Motion of a Rigid Body
Lab #4 - Gyroscopic Motion of a Rigid Body Last Updated: April 6, 2007 INTRODUCTION Gyroscope is a word used to describe a rigid body, usually with symmetry about an axis, that has a comparatively large
More informationRotational & Rigid-Body Mechanics. Lectures 3+4
Rotational & Rigid-Body Mechanics Lectures 3+4 Rotational Motion So far: point objects moving through a trajectory. Next: moving actual dimensional objects and rotating them. 2 Circular Motion - Definitions
More informationChapter 15 Appendix Moment of Inertia of a Spherical Shell
Chapter 1 Appendix Moment of nertia of a Spherical Shell t is common to regard the rotation of a rigid object with spherical symmetry; we live on one such object (not entirely uniform and not entirely
More informationVALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING
VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.
More informationDETAILED SYLLABUS FOR DISTANCE EDUCATION. Diploma. (Three Years Semester Scheme) Diploma in Architecture (DARC)
DETAILED SYLLABUS FOR DISTANCE EDUCATION Diploma (Three Years Semester Scheme) Diploma in Architecture (DARC) COURSE TITLE DURATION : Diploma in ARCHITECTURE (DARC) : 03 Years (Semester System) FOURTH
More informationSolutions to the Exercises of Chapter 5
Solutions to the Eercises of Chapter 5 5A. Lines and Their Equations. The slope is 5 5. Since (, is a point on the line, y ( ( is an ( 6 8 8 equation of the line in point-slope form. This simplifies to
More informationENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 4 COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those studying
More informationCalculus II - Fall 2013
Calculus II - Fall Midterm Exam II, November, In the following problems you are required to show all your work and provide the necessary explanations everywhere to get full credit.. Find the area between
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
More informationMechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics)
Week 7, 14 March Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Ki-Bok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear
More informationTwo Dimensional Rotational Kinematics Challenge Problem Solutions
Two Dimensional Rotational Kinematics Challenge Problem Solutions Problem 1: Moment of Inertia: Uniform Disc A thin uniform disc of mass M and radius R is mounted on an axis passing through the center
More information5 Distributed Forces 5.1 Introduction
5 Distributed Forces 5.1 Introduction - Concentrated forces are models. These forces do not exist in the exact sense. - Every external force applied to a body is distributed over a finite contact area.
More information