2 Exam (Final) - Study Guide
Dynamics, Fall 2006 How to do well on this exam
1. Review your work. Make sure you understand the assigned practice problems and application/design examples. Solutions for the assigned problems are available. 2. Review skills and concepts. Go through the assigned readings concentrating on section and chapter reviews. Think about how the main concepts are applied in the practice, application and design problems. Also read through the Review 1 and Review 2 chapters in the Hibbeler text (we did not cover energy methods or impulse). 3. Practice. Working practice problems, beyond those assigned, will build your condence and improve you skills. Practice problems will be made available 4. Ask for help. If there are concepts you dont understand or problems you are having trouble get help. Come to the review session and bring your questions.
Whats covered on the exam?
Assignments The exam will cover the problem sets, application problems and in-class examples from this semester. The exam will concentrate on the material covered since the rst exam, but the 3D mechanics (kinematics and kinetics) is predicated on your understanding of 2D mechanics. References From the Hibbeler textbook... Chapters: 12, 13, 15.{3,5,6}, 16, 17, 19.{1,3} Chapters: 20, 21.{1, 2, 4, 5, 6} LTI systems from online textbook chapters... Ogata Chapters 1, 2, 8 and 9 Nise Chapter 10 (not we are not covering Bode sketching rules, just the ability to use Bode plots (frequency design) to understand system behavior). Material from class... LTI Examples: practice problems and MATLAB examples.
Format of the exam
The exam is a set of problems similar to the practice problems of the course. There will be between 4 and 6 problems. The weighting of each will be included in the problem statement. In addition to quantitative answers you may be asked to provide brief explanations founded on your knowledge of dynamics. The exam will take place in class during our schedule nal period. You will be provided with the necessary reference materials (moment of inertia tables and Laplace transform properties/pairs). There will also be scratch paper available. Come prepared to work for the entire 3 hours on the exam.
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Learning Objectives
The purpose of this exam is to motivate your assimilation of the skills and concepts necessary for understanding and explaining the dynamics of mechanical systems. You will be successful if you communicate your ability to apply these skills and concepts.
Skills
Problem solving process (coordinates, free-body-diagram, kinematics, kinetics and constitutive relations). Drawing Free Body Diagrams Draw forces and accelerations in directions consistent with the kinematic sign conventions. Applying intermediate reference frames for determining velocity and acceleration. Choosing appropriate locations for your frames reference can aect the complexity of the solution, but many choices will yield the same answer. Applying velocity and acceleration equations to analyze 3D motion.
Concepts
Properties of Rigid Bodies Mass Moment of Inertia Parallel axis theorem Superposition (adding and subtracting mass moments of inertia for composite bodies) 3D inertia tensor (moments of inertia and products of inertia) Kinematics The total derivative - taking the derivative of a vector dened in a rotating reference frame - is necessary for accounting for the rate of change of a vector with respect to an intermediate rotating frame of reference. Intermediate Reference Frames in both 2D and 3D: The velocity (acceleration) of a point with respect to a xed frame may be determined by considering the velocity (acceleration) with that point with respect to an intermediate frame and the translation and rotation of the intermediate frame. You may express a vector (expressed in using any convenient coordinate frame without changing the frame of reference (with respect to.)
Rigid Body Kinetics
The sum of the external forces on a rigid body is equal to the product of the total mass of the body and the acceleration of the center of mass of the body. In order for the sum of the external torques on a rigid body to be equal to the product of the mass moment of inertia and the angular acceleration ( M = I), the external torques and the mass moment of inertial must be found about a point that is either stationary in the inertial frame (eg., the center of rotation) or moving parallel to the total linear momentum of the rigid body (eg., the center of mass). 3D Equations of Motion
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Eulers equations of motion apply ...