Kinetics of Spatial Mechanisms: Kinetics Equation
|
|
- Timothy Flynn
- 5 years ago
- Views:
Transcription
1 Lecture Note (6): Kinetics of Spatial Mechanisms: Kinetics Equation Objectives - Kinetics equations - Problem solving procedure - Example analysis Kinetics Equation With respect to the center of gravity G of a body system, we have the following two sets of equations: Equation (6.1) for force equilibrium and Equation (6.2) for moment equilibrium. It is noted that Equation (6.1) is the vector form and can be extended to 3 scalar equations. Therefore, in total, we have 6 equations, and they describe the relation between the force / moment and linear motion / angular motion. It is further noted that the inertia tensor (moment of inertia and product of inertia) in these equations is with regard to the coordinate system which passes through the center of gravity. According to our previous discussion in lecture note 5, in the moment equation, we could also take any other point, in particular the fixed point (P). When a fixed point is chosen, the form of the moment equation remains to be the same except that G is changed to P in the subscript of items in equation (6.2), which leads to Equation (6.3). We should also note that in Equation (6.3), the inertia tensor is with respect to a coordinate system which passes through point P. F = ma G (6.1) 2 2 M G = I α ( IY I Z ) ωyωz I Y ( α Y ω Z ω ) IYZ ( ωy ωz ) I Z ( α Z + ω ωy ) 2 2 M GY = IYα Y ( I Z I ) ωzω IYZ ( α Z ω ωy ) I Z ( ωz ω ) I Y ( α + ωyωz ) (6.2) 2 2 M GZ = I Zα Z ( I IY ) ω ωy I Z ( α ω Y ωz ) I Y ( ω ωy ) IYZ ( α Y + ωzω ) 2 2 MP = Iα ( IY IZ) ωω Y Z IY( αy ω Zω) IYZ( ωy ωz) IZ( αz + ωωy) 2 2 MPY = I α Y Y ( IZ I) ωω Z IYZ( α Z ω ω Y) IZ( ω Z ω ) IY( α ωω + Y Z) (6.3) 2 2 M = I α ( I I ) ωω I ( α ωω) I ( ω ω) I ( α + ωω ) PZ Z Z Y Y Z Y Z Y Y YZ Y Z Page 1 of 16
2 Problem solving procedure Refer to Example 1 in Appendix A Step 1: Establish a reference coordinate system: x-y-z (A). Usually, we prefer to set up the origin of the coordinate system at the fixed point (point A in Example 1) and to choose the principal axes. Step 2: Establish a separate force diagram. Step 3: Do the analysis of known and unknown variables to confirm if there are six or less six unknowns. Step 4: Establish the force equation ( F = ma G ). There are three scalar equations. Step 5: Select a point and establish the moment equation around the coordinate system that passes through this point. Step 6: Find the expression of a G, including the center of gravity, moment and production of inertia. Example Analysis Appendix A contains two examples. In the first example, the given conditions include the torque on the vertical shaft. When there is a torque applied, there will be usually an angular acceleration; in this case, α z, α z is an unknown variable. Quite often, we may consider α z is zero, which is wrong. So in this example, the unknown variables are: A x, A y, A z, B x, B y, α z (see Appendix A). We should also notice the following ϖ = x y y ( ω, ω, ω ) = (0,0,10) α = α, α, α ) = (0,0, α ) ( x y y z In the second example (see Appendix A), we need to notice the following points: (1) We have two bodies; CD and AB. Their connection is through a pin joint. Page 2 of 16
3 (2) We have a separate force diagram for the rod AB (see Appendix A). There are six unknown variables: Ax, Ay, Az, Mx, My, and T. In summary, there are basically two classes of problems: Class 1: We know the external force and / or torque. We find the acceleration. Class 2: We know the acceleration. We find the external force and / or torque which maintains the acceleration. Both classes of problems find the support force and moment. - End Page 3 of 16
4 Appendix A There are two examples in this appendix. The first problem falls into the class 1, while the second problem falls into the class 2. Page 4 of 16
5 Example 1 Figure A1 Page 5 of 16
6 Figure A2 Page 6 of 16
7 Page 7 of 16
8 Page 8 of 16
9 Page 9 of 16
10 Example 2 Page 10 of 16
11 Example 2 Page 11 of 16
12 Page 12 of 16
13 Page 13 of 16
14 r = (sin 40) iˆ+ (cos 40) ˆj G/ A Page 14 of 16
15 [(sin 40) iˆ+ (cos 40) ˆj]) Page 15 of 16
16 Page 16 of 16
Manipulator Dynamics 2. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA
Manipulator Dynamics 2 Forward Dynamics Problem Given: Joint torques and links geometry, mass, inertia, friction Compute: Angular acceleration of the links (solve differential equations) Solution Dynamic
More information16.07 Dynamics Final Exam
Name:... Massachusetts Institute of Technology 16.07 Dynamics Final Exam Tuesday, December 20, 2005 Problem 1 (8) Problem 2 (8) Problem 3 (10) Problem 4 (10) Problem 5 (10) Problem 6 (10) Problem 7 (10)
More informationLecture 35: The Inertia Tensor
Lecture 35: The Inertia Tensor We found last time that the kinetic energy of a rotating obect was: 1 Trot = ωω i Ii where i, ( I m δ x x x i i, k, i, k So the nine numbers represented by the I i tell us
More informationCenter of Gravity Pearson Education, Inc.
Center of Gravity = The center of gravity position is at a place where the torque from one end of the object is balanced by the torque of the other end and therefore there is NO rotation. Fulcrum Point
More informationEQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS (Section 17.4) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid
EQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS (Section 17.4) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing rotational motion. APPLICATIONS The crank
More informationTorque and Rotation Lecture 7
Torque and Rotation Lecture 7 ˆ In this lecture we finally move beyond a simple particle in our mechanical analysis of motion. ˆ Now we consider the so-called rigid body. Essentially, a particle with extension
More informationRigid Body Dynamics: Kinematics and Kinetics. Rigid Body Dynamics K. Craig 1
Rigid Body Dynamics: Kinematics and Kinetics Rigid Body Dynamics K. Craig 1 Topics Introduction to Dynamics Basic Concepts Problem Solving Procedure Kinematics of a Rigid Body Essential Example Problem
More informationVectors for Physics. AP Physics C
Vectors for Physics AP Physics C A Vector is a quantity that has a magnitude (size) AND a direction. can be in one-dimension, two-dimensions, or even three-dimensions can be represented using a magnitude
More informationAngular Momentum. Physics 1425 Lecture 21. Michael Fowler, UVa
Angular Momentum Physics 1425 Lecture 21 Michael Fowler, UVa A New Look for τ = Iα We ve seen how τ = Iα works for a body rotating about a fixed axis. τ = Iα is not true in general if the axis of rotation
More informationCP1 REVISION LECTURE 3 INTRODUCTION TO CLASSICAL MECHANICS. Prof. N. Harnew University of Oxford TT 2017
CP1 REVISION LECTURE 3 INTRODUCTION TO CLASSICAL MECHANICS Prof. N. Harnew University of Oxford TT 2017 1 OUTLINE : CP1 REVISION LECTURE 3 : INTRODUCTION TO CLASSICAL MECHANICS 1. Angular velocity and
More informationGeneral Physics I. Lecture 10: Rolling Motion and Angular Momentum.
General Physics I Lecture 10: Rolling Motion and Angular Momentum Prof. WAN, Xin (万歆) 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Rolling motion of a rigid object: center-of-mass motion
More information3D Semiloof Thin Beam Elements
3D Semiloof Thin Beam Elements General Element Name Z,w,θz Y,v,θy Element Group X,u,θx Element Subgroup Element Description Number Of Nodes BSL3, BSL4 y 1 4 x z 2 Semiloof 3 Curved beam elements in 3D
More information6. 3D Kinematics DE2-EA 2.1: M4DE. Dr Connor Myant
DE2-EA 2.1: M4DE Dr Connor Myant 6. 3D Kinematics Comments and corrections to connor.myant@imperial.ac.uk Lecture resources may be found on Blackboard and at http://connormyant.com Contents Three-Dimensional
More informationScalar product Work Kinetic energy Work energy theorem Potential energy Conservation of energy Power Collisions
BLOOM PUBLIC SCHOOL Vasant Kunj, New Delhi Lesson Plan Class: XI Subject: Physics Month: August No of Periods: 11 Chapter No. 6: Work, energy and power TTT: 5 WT: 6 Chapter : Work, energy and power Scalar
More informationChapter 11. Angular Momentum
Chapter 11 Angular Momentum Angular Momentum Angular momentum plays a key role in rotational dynamics. There is a principle of conservation of angular momentum. In analogy to the principle of conservation
More information2.003 Engineering Dynamics Problem Set 6 with solution
.00 Engineering Dynamics Problem Set 6 with solution Problem : A slender uniform rod of mass m is attached to a cart of mass m at a frictionless pivot located at point A. The cart is connected to a fixed
More informationClassical Mechanics Lecture 15
Classical Mechanics Lecture 5 Today s Concepts: a) Parallel Axis Theorem b) Torque & Angular Acceleration Mechanics Lecture 5, Slide Unit 4 Main Points Mechanics Lecture 4, Slide Unit 4 Main Points Mechanics
More informationRotational Kinetic Energy
Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body
More informationChapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:
linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)
More informationare (0 cm, 10 cm), (10 cm, 10 cm), and (10 cm, 0 cm), respectively. Solve: The coordinates of the center of mass are = = = (200 g g g)
Rotational Motion Problems Solutions.. Model: A spinning skater, whose arms are outstretched, is a rigid rotating body. Solve: The speed v rω, where r 40 / 0.70 m. Also, 80 rpm (80) π/60 rad/s 6 π rad/s.
More informationDYNAMICS MOMENT OF INERTIA
DYNAMICS MOMENT OF INERTIA S TO SELF ASSESSMENT EXERCISE No.1 1. A cylinder has a mass of 1 kg, outer radius of 0.05 m and radius of gyration 0.03 m. It is allowed to roll down an inclined plane until
More informationLecture 4. Differential Analysis of Fluid Flow Navier-Stockes equation
Lecture 4 Differential Analysis of Fluid Flow Navier-Stockes equation Newton second law and conservation of momentum & momentum-of-momentum A jet of fluid deflected by an object puts a force on the object.
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 informationRigid body simulation. Once we consider an object with spatial extent, particle system simulation is no longer sufficient
Rigid body dynamics Rigid body simulation Once we consider an object with spatial extent, particle system simulation is no longer sufficient Rigid body simulation Unconstrained system no contact Constrained
More informationProf. Rupak Mahapatra. Physics 218, Chapter 15 & 16
Physics 218 Chap 14 & 15 Prof. Rupak Mahapatra Physics 218, Chapter 15 & 16 1 Angular Quantities Position Angle θ Velocity Angular Velocity ω Acceleration Angular Acceleration α Moving forward: Force Mass
More informationFor a rigid body that is constrained to rotate about a fixed axis, the gravitational torque about the axis is
Experiment 14 The Physical Pendulum The period of oscillation of a physical pendulum is found to a high degree of accuracy by two methods: theory and experiment. The values are then compared. Theory For
More informationVideo 2.1a Vijay Kumar and Ani Hsieh
Video 2.1a Vijay Kumar and Ani Hsieh Robo3x-1.3 1 Introduction to Lagrangian Mechanics Vijay Kumar and Ani Hsieh University of Pennsylvania Robo3x-1.3 2 Analytical Mechanics Aristotle Galileo Bernoulli
More information= 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk
A sphere (green), a disk (blue), and a hoop (red0, each with mass M and radius R, all start from rest at the top of an inclined plane and roll to the bottom. Which object reaches the bottom first? (Use
More informationMultibody simulation
Multibody simulation Dynamics of a multibody system (Euler-Lagrange formulation) Dimitar Dimitrov Örebro University June 16, 2012 Main points covered Euler-Lagrange formulation manipulator inertia matrix
More informationRotational motion problems
Rotational motion problems. (Massive pulley) Masses m and m 2 are connected by a string that runs over a pulley of radius R and moment of inertia I. Find the acceleration of the two masses, as well as
More informationNotes on Torque. We ve seen that if we define torque as rfsinθ, and the N 2. i i
Notes on Torque We ve seen that if we define torque as rfsinθ, and the moment of inertia as N, we end up with an equation mr i= 1 that looks just like Newton s Second Law There is a crucial difference,
More informationProblem 1. Mathematics of rotations
Problem 1. Mathematics of rotations (a) Show by algebraic means (i.e. no pictures) that the relationship between ω and is: φ, ψ, θ Feel free to use computer algebra. ω X = φ sin θ sin ψ + θ cos ψ (1) ω
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 informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF
More informationPhysics Waves & Oscillations. Mechanics Lesson: Circular Motion. Mechanics Lesson: Circular Motion 1/18/2016. Spring 2016 Semester Matthew Jones
Physics 42200 Waves & Oscillations Lecture 5 French, Chapter 3 Spring 2016 Semester Matthew Jones Mechanics Lesson: Circular Motion Linear motion: Mass: Position: Velocity: / Momentum: Acceleration: /
More informationGeneral Physics I. Lecture 9: Vector Cross Product. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 9: Vector Cross Product Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Examples of the rotation of a rigid object about a fixed axis Force/torque
More informationLagrange s Equations of Motion and the Generalized Inertia
Lagrange s Equations of Motion and the Generalized Inertia The Generalized Inertia Consider the kinetic energy for a n degree of freedom mechanical system with coordinates q, q 2,... q n. If the system
More informationRigid bodies - general theory
Rigid bodies - general theory Kinetic Energy: based on FW-26 Consider a system on N particles with all their relative separations fixed: it has 3 translational and 3 rotational degrees of freedom. Motion
More informationMECH 5312 Solid Mechanics II. Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso
MECH 5312 Solid Mechanics II Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso Table of Contents Preliminary Math Concept of Stress Stress Components Equilibrium
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 6 Mathematical Representation of Physical Systems II 1/67
1/67 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 6 Mathematical Representation of Physical Systems II State Variable Models for Dynamic Systems u 1 u 2 u ṙ. Internal Variables x 1, x 2 x n y 1 y 2. y m Figure
More informationLecture 38: Equations of Rigid-Body Motion
Lecture 38: Equations of Rigid-Body Motion It s going to be easiest to find the equations of motion for the object in the body frame i.e., the frame where the axes are principal axes In general, we can
More informationLecture 9: Eigenvalues and Eigenvectors in Classical Mechanics (See Section 3.12 in Boas)
Lecture 9: Eigenvalues and Eigenvectors in Classical Mechanics (See Section 3 in Boas) As suggested in Lecture 8 the formalism of eigenvalues/eigenvectors has many applications in physics, especially in
More informationAP Physics QUIZ Chapters 10
Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible
More information1/30. Rigid Body Rotations. Dave Frank
. 1/3 Rigid Body Rotations Dave Frank A Point Particle and Fundamental Quantities z 2/3 m v ω r y x Angular Velocity v = dr dt = ω r Kinetic Energy K = 1 2 mv2 Momentum p = mv Rigid Bodies We treat a rigid
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5
1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 36 EQUATIONS OF MOTION: ROTATION
More informationPhysics 312, Winter 2007, Practice Final
Physics 312, Winter 2007, Practice Final Time: Two hours Answer one of Question 1 or Question 2 plus one of Question 3 or Question 4 plus one of Question 5 or Question 6. Each question carries equal weight.
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 24: Ch.17, Sec.1-3
1 / 38 CEE 271: Applied Mechanics II, Dynamics Lecture 24: Ch.17, Sec.1-3 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, Nov. 13, 2012 2 / 38 MOMENT OF
More informationLecture 20 Chapter 12 Angular Momentum Course website:
Lecture 20 Chapter 12 Angular Momentum Another Law? Am I in a Law school? Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational
More informationPhysics 4A Solutions to Chapter 10 Homework
Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 0-4 (a) positive (b) zero (c) negative (d) negative Q 0-6
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 informationMotion in Space. MATH 311, Calculus III. J. Robert Buchanan. Fall Department of Mathematics. J. Robert Buchanan Motion in Space
Motion in Space MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Background Suppose the position vector of a moving object is given by r(t) = f (t), g(t), h(t), Background
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 16: Euler s Equations Attitude Dynamics In this Lecture we will cover: The Problem of Attitude Stabilization Actuators Newton
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = s = rφ = Frφ Fr = τ (torque) = τφ r φ s F to s θ = 0 DEFINITION
More informationLecture 9 Kinetics of rigid bodies: Impulse and Momentum
Lecture 9 Kinetics of rigid bodies: Impulse and Momentum Momentum of 2-D Rigid Bodies Recall that in lecture 5, we discussed the use of momentum of particles. Given that a particle has a, and is travelling
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx When the mass is released, the spring will pull
More informationPhys 7221 Homework # 8
Phys 71 Homework # 8 Gabriela González November 15, 6 Derivation 5-6: Torque free symmetric top In a torque free, symmetric top, with I x = I y = I, the angular velocity vector ω in body coordinates with
More informationLecture 38: Equations of Rigid-Body Motion
Lecture 38: Equations of Rigid-Body Motion It s going to be easiest to find the equations of motion for the object in the body frame i.e., the frame where the axes are principal axes In general, we can
More informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1
Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid
More informationMCE 366 System Dynamics, Spring Problem Set 2. Solutions to Set 2
MCE 366 System Dynamics, Spring 2012 Problem Set 2 Reading: Chapter 2, Sections 2.3 and 2.4, Chapter 3, Sections 3.1 and 3.2 Problems: 2.22, 2.24, 2.26, 2.31, 3.4(a, b, d), 3.5 Solutions to Set 2 2.22
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More informationα = p = m v L = I ω Review: Torque Physics 201, Lecture 21 Review: Rotational Dynamics a = Στ = I α
Physics 1, Lecture 1 Today s Topics q Static Equilibrium of Rigid Objects(Ch. 1.1-3) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises
More informationRotational Dynamics continued
Chapter 9 Rotational Dynamics continued 9.1 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationModels and Anthropometry
Learning Objectives Models and Anthropometry Readings: some of Chapter 8 [in text] some of Chapter 11 [in text] By the end of this lecture, you should be able to: Describe common anthropometric measurements
More informationRigid Body Dynamics, SG2150 Solutions to Exam,
KTH Mechanics 011 10 Calculational problems Rigid Body Dynamics, SG150 Solutions to Eam, 011 10 Problem 1: A slender homogeneous rod of mass m and length a can rotate in a vertical plane about a fied smooth
More informationIf the symmetry axes of a uniform symmetric body coincide with the coordinate axes, the products of inertia (Ixy etc.
Prof. O. B. Wright, Autumn 007 Mechanics Lecture 9 More on rigid bodies, coupled vibrations Principal axes of the inertia tensor If the symmetry axes of a uniform symmetric body coincide with the coordinate
More informationPhysics 101 Lecture 11 Torque
Physics 101 Lecture 11 Torque Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Force vs. Torque q Forces cause accelerations q What cause angular accelerations? q A door is free to rotate about an axis
More informationRotational Motion. Rotational Motion. Rotational Motion
I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x =
More informationA Miniaturized Satellite Attitude Determination and Control System with Autonomous Calibration Capabilities
A Miniaturized Satellite Attitude Determination and Control System with Autonomous Calibration Capabilities Sanny Omar Dr. David Beale Dr. JM Wersinger Introduction ADACS designed for CubeSats CubeSats
More information20k rad/s and 2 10k rad/s,
ME 35 - Machine Design I Summer Semester 0 Name of Student: Lab Section Number: FINAL EXAM. OPEN BOOK AND CLOSED NOTES. Thursday, August nd, 0 Please show all your work for your solutions on the blank
More informationInertia Forces in a Reciprocating Engine, Considering the Weight of Connecting Rod.
Inertia Forces in a Reciprocating Engine, Considering the Weight of Connecting Rod. We use equivalent mass method. let OC be the crank and PC, the connecting rod whose centre of gravity lies at G. We will
More informationis acting on a body of mass m = 3.0 kg and changes its velocity from an initial
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
More informationAngular Momentum Conservation of Angular Momentum
Lecture 22 Chapter 12 Physics I Angular Momentum Conservation of Angular Momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational
More informationLecture 3 (Scalar and Vector Multiplication & 1D Motion) Physics Spring 2017 Douglas Fields
Lecture 3 (Scalar and Vector Multiplication & 1D Motion) Physics 160-02 Spring 2017 Douglas Fields Multiplication of Vectors OK, adding and subtracting vectors seemed fairly straightforward, but how would
More informationLecture Outline Chapter 11. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 11 Physics, 4 th Edition James S. Walker Chapter 11 Rotational Dynamics and Static Equilibrium Units of Chapter 11 Torque Torque and Angular Acceleration Zero Torque and Static
More informationPhysics 106b/196b Problem Set 9 Due Jan 19, 2007
Physics 06b/96b Problem Set 9 Due Jan 9, 2007 Version 3: January 8, 2007 This problem set focuses on dynamics in rotating coordinate systems (Section 5.2), with some additional early material on dynamics
More informationPhysics A - PHY 2048C
Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
More information( )( ) ( )( ) Fall 2017 PHYS 131 Week 9 Recitation: Chapter 9: 5, 10, 12, 13, 31, 34
Fall 07 PHYS 3 Chapter 9: 5, 0,, 3, 3, 34 5. ssm The drawing shows a jet engine suspended beneath the wing of an airplane. The weight W of the engine is 0 00 N and acts as shown in the drawing. In flight
More informationDynamics. 1 Copyright c 2015 Roderic Grupen
Dynamics The branch of physics that treats the action of force on bodies in motion or at rest; kinetics, kinematics, and statics, collectively. Websters dictionary Outline Conservation of Momentum Inertia
More informationStress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress
More informationPhys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw
Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the
More informationMECHANICS OF MATERIALS Design of a Transmission Shaft
Design of a Transmission Shaft If power is transferred to and from the shaft by gears or sprocket wheels, the shaft is subjected to transverse loading as well as shear loading. Normal stresses due to transverse
More informationDynamical Systems & Lyapunov Stability
Dynamical Systems & Lyapunov Stability Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Ordinary Differential Equations Existence & uniqueness Continuous dependence
More informationRotational N.2 nd Law
Lecture 0 Chapter 1 Physics I Rotational N. nd Law Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics Today
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
More informationLectures. Today: Rolling and Angular Momentum in ch 12. Complete angular momentum (chapter 12) and begin equilibrium (chapter 13)
Lectures Today: Rolling and Angular Momentum in ch 1 Homework 6 due Next time: Complete angular momentum (chapter 1) and begin equilibrium (chapter 13) By Monday, will post at website Sample midterm II
More informationLecture 14. Rotational dynamics Torque. Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
Lecture 14 Rotational dynamics Torque Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes, 87 1 BC EXAM Tuesday March 6, 018 8:15 PM 9:45 PM Today s Topics:
More informationPhysics 201, Lecture 21
Physics 201, Lecture 21 Today s Topics q Static Equilibrium of Rigid Objects(Ch. 12.1-3) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises
More informationPHY 5246: Theoretical Dynamics, Fall Assignment # 10, Solutions. (1.a) N = a. we see that a m ar a = 0 and so N = 0. ω 3 ω 2 = 0 ω 2 + I 1 I 3
PHY 54: Theoretical Dynamics, Fall 015 Assignment # 10, Solutions 1 Graded Problems Problem 1 x 3 a ω First we calculate the moments of inertia: ( ) a I 1 = I = m 4 + b, 1 (1.a) I 3 = ma. b/ α The torque
More informationCHAPTER 9 ROTATIONAL DYNAMICS
CHAPTER 9 ROTATIONAL DYNAMICS PROBLEMS. REASONING The drawing shows the forces acting on the person. It also shows the lever arms for a rotational axis perpendicular to the plane of the paper at the place
More informationHandout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a
More informationChapter 9- Static Equilibrium
Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h
More informationω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2
PHY 302 K. Solutions for problem set #9. Textbook problem 7.10: For linear motion at constant acceleration a, average velocity during some time interval from t 1 to t 2 is the average of the velocities
More informationThe acceleration due to gravity g, which varies with latitude and height, will be approximated to 101m1s 2, unless otherwise specified.
The acceleration due to gravity g, which varies with latitude and height, will be approximated to 101m1s 2, unless otherwise specified. F1 (a) The fulcrum in this case is the horizontal axis, perpendicular
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :
More informationKinetic Energy of Rolling
Kinetic Energy of Rolling A solid disk and a hoop (with the same mass and radius) are released from rest and roll down a ramp from a height h. Which one is moving faster at the bottom of the ramp? A. they
More informationRotational N.2 nd Law
Lecture 19 Chapter 12 Rotational N.2 nd Law Torque Newton 2 nd Law again!? That s it. He crossed the line! Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will
More informationSolution to phys101-t112-final Exam
Solution to phys101-t112-final Exam Q1. An 800-N man stands halfway up a 5.0-m long ladder of negligible weight. The base of the ladder is.0m from the wall as shown in Figure 1. Assuming that the wall-ladder
More information2.003 Engineering Dynamics Problem Set 4 (Solutions)
.003 Engineering Dynamics Problem Set 4 (Solutions) Problem 1: 1. Determine the velocity of point A on the outer rim of the spool at the instant shown when the cable is pulled to the right with a velocity
More informationLAWS OF GYROSCOPES / CARDANIC GYROSCOPE
LAWS OF GYROSCOPES / CARDANC GYROSCOPE PRNCPLE f the axis of rotation of the force-free gyroscope is displaced slightly, a nutation is produced. The relationship between precession frequency or nutation
More information