PHY321W08MT1Soln

# PHY321W08MT1Soln - PHY 321 Midterm 1 Winter 2008 Time...

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Unformatted text preview: PHY 321 Midterm 1 Winter 2008 Time allowed: 65 minutes Show details for partial credit 0o ,t‘a a Skfew~\$ywaneélh>3~ m1 5(va x . «.n—w‘" U— is“; .gga v . am it VMFﬁ g: .5; F5 62, 1. Consider an orthonormal frame (e’l, 8/2) rotated from another orthonormal T .3 "’ frame (61, 62) in the counterclockwise sense by 7r/4. Write , V 7 - 6’ 61 = (Li 6;- . “Z . . 1 Give the matrix (a3 ) explicitly ‘4“ t W 6 2. The matrix representation of a linear transformation 011 R2 with respect I to an orthonormal frame (61,62) is given by ' 1 0 AI = (O 2) . T 55 “7118.13 is the matrix representation .M’ with respect to (6’1, 8’2)7 related to (61, 82) as in Problem 1? Q _ I85 I . Write A- (B x C ) in terms of the Levi-Givita tensor and the components of A, B and C. . Consider a ﬁxed orthonormal frame ((51, 52, 63) and a moving orthonormal ' 9% frame (61,63, 63). Suppose ' “' ei = aj 6‘ and (lei 2‘ wj ej (3> 1‘3» 1' - ‘ A- Write Log in terms of the (Li. Give a general property of the matrix of ‘ Pr j , i. 1—forms w . A particle of mass 1 Kg is moving along a longitude line on the surface of a sphere of radius 1 m. The polar angle changes according to 0(t) : 1 + 2t + tg/G (t in seconds) . At t = 1 sec., what are the forces FT and F9 acting on the particle along er and 69, respectively? . A cone of height h =2 1 111 is rotating about a ﬁxed axis with constant angular speed to : \/§ 3‘1 (as shown). The axis of rotation lies on the y—z plane. When the point A on the cone is also on the y-z plane7 what is its velocity 11? (Give the x, y, 2 components.) @ FEESXV 7‘“ '“ m; w...) . £3 a" :7. 5) (,0 Zﬁgéﬂ‘iﬁ-O “gt-W661i?) 3“ é a P, A : i} ia a :9. .4 - a ‘5 A g. f- r: .33.“, (but: 611‘ j “i' 674” 5‘5" 'i' ii My rﬁf\ ‘ ’ ta 3 3 51 it. .... "am i. 3 l3: A I o 7 :i A 1% 0 "i l i I J m (owe if.) 7. Is the force ﬁeld EC; + N 11> conservative? W hy? 8. State the diﬁerential form or" the equation of continuity (involving the current density J and the mass density p), and use Gauss’ theorem to write its integral form (involving volume and surface integrals). Give a physical interpretation of the integral form (a picture may help). i m x ‘f a: a i F 2: v’ :_ 0 v/ZFZO‘M 50:5“. :9; CJMWA m4 ” 2f wasmm (I ll 5' " 3.» KL Ll?’ Ed“ ix I?) 42’ LEASEW"\$"€ wig” ) ’ ' ‘r is, Cﬁrwafﬁzh Mia UM {H‘Kﬁanwuav Il/ltuﬁ ‘w‘ 1“: {13H “mama m. 2 y ,, {r1 ski .. ...
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## This note was uploaded on 06/10/2008 for the course PHY 321 taught by Professor Lam during the Spring '08 term at Cal Poly Pomona.

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PHY321W08MT1Soln - PHY 321 Midterm 1 Winter 2008 Time...

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