phys1441-spring08-041608-post

phys1441-spring08-041608-post - PHYS 1441 Section 002...

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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 1 PHYS 1441 – Section 002 Lecture #22 Wednesday, Apr. 16, 2008 Dr. Jae hoon Yu Moment of Inertia Work, Power and Energy in Rotation Rotational Kinetic Energy Angular Momentum and Its Conservation Similarity of Linear and Rotational Quantities Simple Harmonic Motion
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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 2 Announcements •3 rd term exam – 1 – 2:20pm, Next Monday, Apr. 21 – Covers: Ch. 6.7 – 9.6 – Practice problems can be downloaded from my home page: http://www-hep.uta.edu/~yu/ch06-practice.pdf http://www-hep.uta.edu/~yu/ch07-practice.pdf http://www-hep.uta.edu/~yu/ch08-practice.pdf http://www-hep.uta.edu/~yu/ch09-practice.pdf – This is the final term exam in the semester – The worst of the three term exams will be dropped from the final grading Final Exam – Comprehensive exam: CH1.1 – what we can cover on Apr. 23 • Jason will conduct review on Apr. 28 and Apr. 30 in preparation for this exam – Time and date: 11am – 12:30 pm, Monday, May 5 – Place: SH103 Colloquium today at 4pm in SH101 – Dr. Nail Fazleev of UTA Physics
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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 3
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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 4 Moment of Inertia Rotational Inertia: What are the dimension and unit of Moment of Inertia? I 2 m kg [ ] 2 ML Measure of resistance of an object to changes in its rotational motion. Equivalent to mass in linear motion. Determining Moment of Inertia is extremely important for computing equilibrium of a rigid body, such as a building. I For a group of objects For a rigid body 2 ii i mr 2 rdm Dependent on the axis of rotation!!!
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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 5 Two particles each have mass and are fixed at the ends of a thin rigid rod. The length of the rod is L . Find the moment of inertia when this object rotates relative to an axis that is perpendicular to the rod at (a) one end and (b) the center. Ex. 9 The Moment of Inertia Depends on Where the Axis Is. (a) I = 1 0 r = 12 mm m == I = (b) I = 1 2 rL = m I = 2 = 2 mL () ( ) 22 0 L += 2 mr = 11 2 2 mr + 2 = + 2 2 = mL 2 1 2 mL Which case is easier to spin? Case (b) Why? Because the moment of inertia is smaller
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Wednesday, Apr. 16, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 6 Example for Moment of Inertia In a system of four small spheres as shown in the figure, assuming the radii are negligible and the rods connecting the particles are massless, compute the moment of inertia and the rotational kinetic energy when the system rotates about the y-axis at angular speed ω . I Since the rotation is about y axis, the moment of inertia about y axis, I y , is R K Thus, the rotational kinetic energy is Find the moment of inertia and rotational kinetic energy when the system rotates on the x-y plane about the z-axis that goes through the origin O.
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phys1441-spring08-041608-post - PHYS 1441 Section 002...

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