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hw7_ocw

# hw7_ocw - matrix for this system(b Find the angular...

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± ± ± 16.61 Handout #7 Prof .J. P .How April 3, 2003 Prof. J. Deyst Due: April 10, 2003 16.61 Homework Assignment #7 1. In the March 2001 edition of the National Geographic magazine, one of the questions to the Ask us column is Is it true that when you ﬂush a toilet, water circulates clockwise in the Northern Hemi­ sphere and counterclockwise in the Southern Hemisphere? What do you think led the reader to ask this question, and what would your answer be, and why? 2. Consider a body with 30 I xy I xz I = 10 20 I yz 0 I zy 30 and angular velocity ω =10 ± i +10 ± j +10 ± k If H = 200 ± i + 200 ± j + 400 ± k Find: (a) Values for I zy , I xy , I xz , I yz (b) The moment of inertia about ω (c) Rotational kinetic energy (d) Principal moments of

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3. Consider a solid, uniform cube (mass M ) with sides a ,2 a ,and 3 a as shown in the ﬁgure. The body is rotating in such a way that the angular velocity vector passes through the diagonal as shown. (a) Find the inertia
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Unformatted text preview: matrix for this system. (b) Find the angular momentum vector for this system. 4. A thin rod of mass m and length l is balancing vertically on a smooth horizontal ﬂoor. It is disturbed slightly and falls. (a) Given that the rod is a rigid body (6 degrees of freedom) explain why there is only one degree of freedom in this problem. (i.e. List the 5 constraints.) (b) Derive an expression for the motion of the rod by: • Using θ as the generalized coordinate, • Finding T and V , • Finding L , the Lagrangian Function, and • Applying Lagrange’s Equation to solve for the equation of motion in terms of θ and it’s time derivatives. 2...
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hw7_ocw - matrix for this system(b Find the angular...

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