READING QUIZ The theorems of Pappus Guldinus are used to find A)the location of the centroid of any object of revolution. B)the volume of any object of.

Slides:

Advertisements

Similar presentations

Distributed Forces: Centroids and Centers of Gravity

Advertisements

STATIKA STRUKTUR Genap 2012 / 2013 I Made Gatot Karohika ST. MT.

7 STATICS ENGINEERS MECHANICS Theorems of Pappus-Guldinus CHAPTER

Key Concept 1. Key Concept 2 Key Concept 3 Key Concept 4.

Earth is constantly moving in two ways.

7-4 Evaluating and Graphing Sine and Cosine Objective: To use reference angles, calculators or tables, and special angles to find values of the sine and.

Geometry End-Of Course Testing. Multiple Choice Which expression represents the perimeter, in centimeters, of the triangle? A √5 B √20 C.12.

Review: Volumes of Revolution. x y A 45 o wedge is cut from a cylinder of radius 3 as shown. Find the volume of the wedge. You could slice this wedge.

Trig Values of Any Angle Objective: To define trig values for any angle; to construct the “Unit Circle.”

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, B Volumes by the Washer Method Limerick Nuclear Generating Station,

Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

READING QUIZ The mass moment of inertia of a body is defined as I =  r 2 dm. In this equation, r is the A)radius of gyration. B)largest dimension of the.

READING QUIZ For a two-dimensional area contained in the x-y plane, the moment of inertia about the x-axis is represented by A)  y 2 dA. B)  x 2 dA.

READING QUIZ For a composite body, the center of gravity coincides with the centroid of the body if A) the composite body is made of simple geometric shapes.

READING QUIZ 1.For a composite area, the moment of inertia equals the A)vector sum of the moment of inertia of all its parts. B)algebraic sum of the moments.

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 4 – Radians, Arc Length, and Angular Speed.

Finding angles with algebraic expressions

Today’s Objectives: Students will be able to:

According to properties of the dot product, A ( B + C ) equals _________. A) (A B) +( B C) B) (A + B) ( A + C ) C) (A B) – ( A C) D) ( A B ) + ( A C) READING.

13.2 Angles and Angle Measure

Licensed Electrical & Mechanical Engineer

A cube has a total surface area of 24 cm2

Rotations and Compositions of Transformations

Geometry Never, never, never give up. Winston Churchill Today:  9.4 Instruction  Practice.

1 What is the slope of the line represented by the equation A. B. C. D.

Engineering Mechanics: Statics

Partner A Quizzes Partner B. 1) If the graph of the function y = 0.4x is show below: If the graph is translated up 6 units, what will be the new.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–3) NGSSS Then/Now New Vocabulary Key Concept: Glide Reflection Example 1: Graph a Glide Reflection.

9.3 Composite Bodies Consists of a series of connected “simpler” shaped bodies, which may be rectangular, triangular or semicircular A body can be sectioned.

Copyright © 2010 Pearson Education South Asia Pte Ltd

Finding Volumes Disk/Washer/Shell Chapter 6.2 & 6.3 February 27, 2007.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–3) CCSS Then/Now New Vocabulary Key Concept: Glide Reflection Example 1: Graph a Glide Reflection.

X AND Y INTERCEPTS. INTERCEPT  In a function, an intercept is the point at which the graph of the line crosses an axis.  If it crosses the y-axis it.

Using our work from the last few weeks,

13-3 Radian Measure Today’s Objective: I can measure an angle in radians.

9.6 Fluid Pressure According to Pascal’s law, a fluid at rest creates a pressure ρ at a point that is the same in all directions Magnitude of ρ measured.

READING QUIZ A wedge is a __________. A) truss B) frame C) machine D) beam.

8.2 Area of a Surface of Revolution

Moments, Center of Mass, Centroids Lesson 7.6. Mass Definition: mass is a measure of a body's resistance to changes in motion  It is independent of a.

Trigonometry Exact Value Memory Quiz A Trigonometry Exact Value Memory Quiz A.

VOLUME FINAL REVIEW 1) Which statement best describes how the volume of a cube changes when the edge length is tripled (increased by a scale factor of.

Angular Motion. Linear to Angular conversions x Where x = arc length Θ is the angle r is the radius of the circle Linear to angular ( Θ is in radians)

CHAPTER 9.3 AND 9.4 Rotations and Compositions of Transformations.

Chapter 8 – Further Applications of Integration

Applications of Integration 7 Copyright © Cengage Learning. All rights reserved.

COMPLEX NUMBERS and PHASORS. OBJECTIVES  Use a phasor to represent a sine wave.  Illustrate phase relationships of waveforms using phasors.  Explain.

STROUD Worked examples and exercises are in the text Programme 23: Polar coordinate systems POLAR COORDINATE SYSTEMS PROGRAMME 23.

Volume: The Disk Method. Some examples of solids of revolution:

STROUD Worked examples and exercises are in the text Programme 20: Integration applications 2 INTEGRATION APPLICATIONS 2 PROGRAMME 20.

9.3 – Perform Reflections. Reflection: Transformation that uses a line like a mirror to reflect an image Line of Reflection: Mirror line in a reflection.

Concept. Example 1 Graph a Glide Reflection Quadrilateral BGTS has vertices B(–3, 4), G(–1, 3), T(–1, 1), and S(–4, 2). Graph BGTS and its image after.

INTRODUCTION TO DYNAMICS ANALYSIS OF ROBOTS (Part 1)

7.2 Volume: The Disc Method The area under a curve is the summation of an infinite number of rectangles. If we take this rectangle and revolve it about.

10.3 Parametric Arc Length & Area of a Surface of Revolution.

Lecture 6 (II) COMPLEX NUMBERS and PHASORS. OBJECTIVES A.Use a phasor to represent a sine wave. B.Illustrate phase relationships of waveforms using phasors.

MATH 1330 Section 4.3 Trigonometric Functions of Angles.

VOLUME / SA FINAL REVIEW 1) Which statement best describes how the volume of a cube changes when the edge length is tripled (increased by a scale factor.

Measures of Angles and Rotations. Vocabulary Degrees  360 degrees makes a full circle  270 degrees makes a three quarter circle  180 degrees makes.

Revolutions, Degrees and Radians Lesson 40. LESSON OBJECTIVE: 1.Use radian and degree measures to measure angles and rotations. 2.Investigate how radians.

Applications of Integration Copyright © Cengage Learning. All rights reserved.

7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington(Photo not taken by Vickie Kelly)

Chapter 2 Section 1.

Chapter 2 Section 1.

Integration Volumes of revolution.

Engineering Mechanics

Standard Position, Coterminal and Reference Angles

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Area of a Surface of Revolution

Engineering Mechanics : STATICS

Presentation transcript:

READING QUIZ The theorems of Pappus Guldinus are used to find A)the location of the centroid of any object of revolution. B)the volume of any object of revolution. C)the surface area of any object of revolution. D)the volume and surface area of any object of revolution.

READING QUIZ The Pappus theorem expresses the volume of revolution as V =  r A. The  in this equation is the A)angle of revolution measured in degrees. B)angle of revolution measured in radians. C)slope of the area A. D)None of the above.

CONCEPT QUIZ Select the FALSE statement. A)The Pappus theorem can be applied only to volumes or surfaces produced by revolution about an axis. B)The Pappus theorem theorem can not be applied to composite bodies. C)The Pappus theorem is an exact method. D)The angle of revolution  can be any angle between 0 and 2  radians.

ATTENTION QUIZ The volume produced by a 360° rotation of the triangular area about the x-axis is ___. A) 90  in 3 B) 54  in 3 C) 126  in 3 D) 108  in 3 6” 3” x y y x

ATTENTION QUIZ The surface area produced by a 360° rotation of the line shown about the y–axis is ___. A) 30  in 2 B) 25  in 2 C) 50  in 2 D) 10  in 2 1” 5” x 1” 4” 5” 1”