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Unformatted text preview: PHY 321 Midterm 1 Winter 2008
Time allowed: 65 minutes
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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 LeviGivita 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 yz plane7 what is its
velocity 11? (Give the x, y, 2 components.) @ FEESXV 7‘“ '“ m; w...) . £3 a"
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My rﬁf\ ‘ ’
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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
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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.
 Spring '08
 LAM
 mechanics

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