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Express the unit vectors, , φ in terms of 8,9, 2 (that is, derive Eq. 1.64)....
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the cross products #x f, #x θ, PX φ, θ 0, θ >< φ, and φ >< φ. (b) Express x, y and z in terms of, О and ф. (c) Check the divergence theorern for the function u = r , using for volume the sphere of radius 13] R, centered at the origin, i.e. show that dä -JyV-üö)dr.
5. This problem uses cylindrical coordinates. (a) Express x, y and z in terms of unit vectors in cylindrical coordinates s, ф and г. (b) Find the divergence of the function u = s(2 + sín2ф)s + s sin φ cos φ φ + 322, [3] 13)
1) Find the expressions for the unit vectors in cylindrical coordinate system, p, φ,2. in terms of x, ý, 2. Find the time-derivative of each. Hints: Unit vector p is defined in (x, y) plane. Remember that α -φ is perpendicular to a The easiest way to find φ is to express ρ through φ and add 90 degrees
plain why the cosine series is not included in Eq. (5.23) to express the tion on a cambered airfoil. y distribu Circulation Distribution for the Cambered Airfoil s.6 143 istribution for the symmetrical airfoil as given by Eq. (5.11). This part is the form of the γ written 2V-A, ltcose later that A,-α when the airfoil is symmetrical; that is, when dzidr ofthe γ distribution depends only on the shape of the mean camber line here including the point at...
(f) If a and b are unit vectors and θ is the angle between them. prove that sin -b Prove that v2·“2 + 2,6 , where the symbol's h) have their usual meanings 12. Find the following dx dx tan'xdx (i) 1+cos x 13 Find the area enclosed between the circle 2y25 and the straight line x +y- s 14. Solve the following equations dy dy dy dx (f) If a and b are unit vectors and θ is the...
1. This quasi-"walkthrough" problem is great practice in cross-products, vectors, and integration. Consider the current loop shown in Figure 2, with B _Bx, and the loop lying in the x - z plane of the page (y points into the page). We wish to find the net torque on this current loop. we'll do this by integrating in θ, the angle shown (a) We'll start with a little segment dl at point p as shown in the figure. What is...
019.09 points | Previous Answers SerCP9 1.AE.009 EXAMPLE 1.9Cartesian and Polar Coordinates GOAL Understand how to convert from plane rectangular coordinates to plane polar coordinates and vice versa. y (m) PROBLEM (a) The Cartesian coordinates of a point in the xy-plane are (x,y) (-3.50 m, -2.50 m), as shown in the NY figure. Find the polar coordinates of this point. (b) Convert (r, θ) = (5.00 m, 37.0°) to rectangular coordinates x (m) (-3.50,-2.50) STRATEGY Apply the trigonometric functions and...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need background information to answer the questions. The prelab questions are in the 3rd photo. this where we put in the answers, just to give you an idea. Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
please answer all pre-lab questions 1 through 5. THANK YOU!!! this is the manual to give you some background. the pre-lab questions.. the pre-lab sheet. Lab Manual Lab 10: String Waves & Resonance Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and follow the procedure to do the experiment. You will record data sets, perform analyses, answer questions, and...