Question

Problem 1 Answer the following questions T (true) or F (false). Place your answer in the space proviled. (+2 points for correct answers, -I for incorrect answers.) 1) The inertla tensor of a rigid body can only be diagonalizel if the rigid body is symnetric unler rotation alout at least one body axis. 2) The order in wlich we make Euler angle rotations is not important, only the mngnitude of theEuler angles coumit. 3) Multiplication of the Lagrangian by a constant does not affect the equations of motion. 4) The condition that the Lagrangian does not explicit v depend on time implies that the Hamiltonian is the total enera 5) In an incompressible ideal fluid Vx vis always zero. 6 A wave packet rnade up of waves governed by a dispersion relatou of the form w = ck, where c is n constant will mnintain its initial shape. T) The ayleigh-Ritz Variationnl Principle aways gives an estimate of the lowest cigenfroquency of an oscillatory system which is greater than or equal to the actual lowest cigenfrequeucy s ktiza beity witihn o rsistine torqus acting, can rotate stabily oniy about the principl avis with maxlinum moment of inertia. ) The principle of supcrposition is applicable to systems described by lienr equations 10) The most general solution to the wave equation for a tiniforni string of infinite length isq r, t where f(z) is the displacement at t 0. Ur-e) / r + ct

solve each part of the problem separately and indicate your answer clearly to each part of the problem with solutions

Answer 1

Date (1) The nexa tensor ot a 9uqid body Can ohlybe dliagonalizod u Unde otation about at least one booly aus Inera ae always → False

Euler angle suotartion is mot importanh only the mognituole os the Eulen angles tount. 1. Tuul Rotation Cam be dene is any otaHo Osder X, y,z) etc

Date the lagrangian-bi-a ③一ーMultiplication at Constant olaes mot aftect th eg o Motion od Constont thon ean Mution uiu nemain Constant Conolition that Lagrangian a 4 The Lonottion that hagranaian Gonstent loes mot explicitly dep On time ies that the Hamiltonian is the total energ'y endls H Hamiltonjan V Potential emergy

Date dl d a