ES 12: Dynamics of Rigid Bodies First Semester‚ 2012-2013 Due: October 5‚ 2012/ Class Hours PROBLEM SET FOR LQ4 Instructions: 1. Answer this problem set at the back page of used short/A4 size bond paper. 2. At the TOPMOST portion of the first page of your answer sheets‚ write the following: “I hereby certify that I have worked on this problem set by my own honest effort‚ without giving or receiving any inappropriate help. I understand that any evidence which contradicts the foregoing statement
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Where P is the applied force‚ L is the length of beam‚ E is the modulus of elasticity of aluminum‚ and I is the moment of Inertia. For a beam of rectangular cross section‚ say of width w and thickness t‚ the same mid spam deflection of the centrally loaded beam when the flat side is supported‚ then be compared to that when the thin side is supported. The moment of inertia for the respective situations are given by: I1 = wt3/12 and I2 = w3t/12 It could be readily verified that the later situation
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. . . . . . . . . . . . . . . . . . Hoop‚ Disk‚ Cylinder and Sphere . . . . . . . . . . . . . . . . 11 11 13 14 15 17 18 18 19 20 22 24 24 26 27 28 28 30 5 Height of Water in Tank 6 Bead Sliding on Wire 7 James Bond’s Ski Saga 8 Moment of Inertia 8.1 8.2 8.3 8.4 Constant Moment Arm . . . . . . . . . . . . . . . . . . . . . . Moment of Disk or Solid Cylinder About Axis . . . . . . . . Moment of Thin Spherical Shell About Axis . . . . . . . . . . Moment of Solid Sphere About Axis . . . . .
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velocity and its moment of inertia. Just as a moving object’s inertial mass is a measure of its resistance to linear acceleration‚ a rotating object’s moment of inertia is a measure of its resistance to angular acceleration."2 Factors which effect a rotating object’s moment of inertia are its mass and on the distribution of the objects mass about the axis of rotation. A small object with a mass concentrated very close to its axis of rotation will have a small moment of inertia and it will be fairly easy
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EXERCISE 8 - Rotational Dynamics‚ Equilibrium of rigid body 1. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 40.0 N m‚ what minimum force must be exerted by the mechanic at the end of a 30.0-cm lug wrench to accomplish the task? 133 N 2. A steel band exerts a horizontal force of 80.0 N on a tooth at point B in Figure 1. What is the torque on the root of the tooth about point A? 0.64 Nm 3. Calculate the net torque (magnitude and
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Anatomical Analysis Tae Kwon Do is a Korean‚ unarmed martial art and is best known for its kicks (Park‚ 2001). The roundhouse kick is a turning kick and happens to be the most commonly used kick during competition (Lee‚ 1996). For this reason‚ the roundhouse kick will be analyzed in reference to sparring competition. The roundhouse kick‚ a multiplanar skill‚ starts with the kicking leg traveling in an arc towards the front with the knee in a chambered position (Pearson‚ 1997). The knee is extended
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Chapter 11 Rolling‚ Torque‚ and Angular Momentum In this chapter we will cover the following topics: -Rolling of circular objects and its relationship with friction -Redefinition of torque as a vector to describe rotational problems that are more complicated than the rotation of a rigid body about a fixed axis -Angular momentum of single particles and systems of particles -Newton’s second law for rotational motion -Conservation of angular momentum -Applications of the conservation of angular
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sin (θ ) ̈where: m = gymnast body mass g = acceleration due to gravity r = pendulum length (θ ) ̈= angular deviation from the vertical or handstand point This torque results in a rotational acceleration ((θ ) ̈) modulated by the moment of inertia (I(θ ) ̈= mr2(θ ) ̈). The system can therefore be described by the following equation (θ ) ̈+ g/r sin Θ = 0 To achieve the backward giant circle energy lost to frictional forces and the conversion of energy must be overcome. The gymnast achieves
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SYSTEM OF PARTICLES AND ROTATIONAL MOTION CENTRE OF MASS AND ROTATIONAL MOTION INTRODUCTION- For describing the motion of rigid bodies‚ we shall introduce the key concept of ‘centre of mass’. This concept enables us to understand how we can apply justifiably the Newton’s laws of motion‚ in essentially the same form to objects of large size including even the astronomical objects like the planets and the stars. KINDS OF MOTION OF A RIGID BODY- A rigid body may have three kinds of motion- (1) Pure
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Basics of Fluid Mechanics Genick Bar–Meir‚ Ph. D. 2729 West Jarvis Ave Chicago‚ IL 60645-1335 email:barmeir at gmail.com Copyright © 2010‚ 2009‚ 2008‚ 2007‚ and 2006 by Genick Bar-Meir See the file copying.fdl or copyright.tex for copying conditions. Version (0.2.4 March 2‚ 2010) ‘We are like dwarfs sitting on the shoulders of giants” from The Metalogicon by John in 1159 CONTENTS Nomenclature GNU Free Documentation License . . . . . . . . . . . . . . . . 1. APPLICABILITY AND DEFINITIONS
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