test2 - Fall 2011 AAE 340 — Dynamics and Vibrations Exam...

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Unformatted text preview: Fall 2011 AAE 340 — Dynamics and Vibrations Exam II Solufi'on 5 Please read the problems carefully. Write clearly and use diagrams when necessary. ( 30 points) 1. A dumbbell consists of two particles A and B ( of equal mass m) connected by a rigid massless rod of length L. Particle A is constrained to move on a fixed, frictionless circular track centered at point 0 and of radius R. The system moves on a smooth, HORIZONTAL surface. Both angles are free. A A u. r, \ w n B :96an A X ’8 A /\ ‘ a \K a; e: memol \( a A . . xx A u“ a in A em/”" in“ ra’ A A a ’ w“/ "N ERR A ‘2 z m Pod Jig/f ; x\\:\ 81 :1 = Chm 1'33) Us. €~DL ° /\ 5’ g ¢ ’31 = “5,2,0” +Cfl>ug “— *' l“ ' A g m————’ g ()3 : (5 (L3 l“ I} A an A 8 —- Y‘ o . A :K\ //// ¢ w :( + @)u5 I (b A \ \xNiN fix] ’/ (a) Sketch the FBD. (b) Energy is constant. Justify this statement. Write an expression for E. (c) Total linear momentum is NOT constant. Why? (d) Total angular momentum about point 0 is a constant. Justify this statement. N unknown normal clue +0 ‘h‘ctCK WA ) NA all, V73 QB 10 Pm 07C MD‘hOn (b) En ‘ Condan‘b 6.936% A ’ /\ mN-v =Nw+R¢u&~—‘o VN=O normafl 40mg claw no leA (it) Any {owes normafl +0 plane of: War/H do no room (anfl We m ('23 dwwfim) (CM {minimal “Force in rod does no work smce, du‘sw‘omae t)an parfl‘dcs is fixed E=~7> 55m (avAfv’m imfiv‘i We) 6.. O A VA s R¢ Ola .. A .. c . _ A r05: + LY“: "7 avg: R¢Q§U + L(¢ +gp)r~& 5-5 . A o o a A v = chspn + [Wow L(¢+p):} Fa ( 45 points ) 2. Use the force equation and the moment about A to derive the EOM for the system of particles in Probleml. _. cm A PC : Ralf/4‘ A 3V0“: twigs EGIHEWV €~Ocm av . co ,0 A ‘ ' a" A A = R915 52— Rqflf, -+ 5w Hm. - 5015+?) *7 2 [w R931“ " S Cé+fl3>Kij (2| + I R¢>+ itwgm — 5C0; m-yegfig a”; ’- ’\ = NIL: ORA EAcmx am 4 =59, >< am (Raul—Res my : [mLRc'fi’qb + mLRgéa‘sfbl {1‘3 a): so = mLQCéS'+E>S)+mLR<}5'C(5+ mLRgfi'Qsfl) \EOM ( 25 points ) 3. In the figure, a circular disk D rotates at the end of an arm at the constant rate Q rad/s; the arms passes through the disk center of mass. The arms rotates about the inertially-fixed axis é2 at the arbitrary rate 7. (a) Define the appropriate sets of unit vectors. Write the unit vector relationships. (b) Determine the number of degrees of freedom. Use the disk center of mass as the base point and justify your answer. ’Derh‘ne é: that‘fiO/Q 5t: thud in arm 0AM fixed in dtsK 2191‘sk— MM EDP —‘~‘ (p Trans 30F choose am as béléé JOOWC ._. /\ flooofm gm roam = flail/4r L414 A 3 consMVYfie: ‘5» = 920 h 01) L = Lo Role boll 0762M ch3~l< (Home am 1~9\“3 6 Oxbowt at 3 /\ 04 wow} d& /\ (9 WM 0L5 ConSNwhfi: o< = 0(0 ~ 3 fl? 3 (50 e=fl£+50 O Rot 30F ...
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test2 - Fall 2011 AAE 340 — Dynamics and Vibrations Exam...

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