final_f06

final_f06 - 1.053J/2.003J Dynamics and Control I Fall 2006...

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1.053J/2.003J Dynamics and Control I Fall 2006 Final Exam 20 th December, 2006 Important Notes: 1. You are allowed to use three letter-size sheets (two-sides) of notes. 2. There are five problems on the exam for a total of 100 points. The points awarded for each problem are indicated at the top. 3. You have 180 minutes. Cite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2.003J/1.053J Dynamics and Control I, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Problem 1: Non-uniform disc (20 points) Figure 1 A non-uniform disc of mass m and radius r has its center of mass C at a distance d from the center of the disc Q , as shown in figure 1. The disc rolls on the horizontal surface without slippage. Initially, the disc is oriented such that C lies vertically below Q , after which it is perturbed and starts rolling. Let θ be the instantaneous angle that the segment QC makes with the vertical direction, measured in the anti-clockwise direction as shown in the figure, and let I be the moment of inertia of the disc about point C. Note that gravity acts. a. In terms of θ and its derivatives θ and , find the acceleration of C with respect to a frame that is fixed to the ground. Now use the Newtonian method (linear and angular momentum equations) to derive the equation of motion for the system as follows. b. Can you use the torque equation about the instantaneous center of rotation (ICR)? Explain.
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final_f06 - 1.053J/2.003J Dynamics and Control I Fall 2006...

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