Q.1
a) Calculate the scale factors for the cylindrical and spherical coordinate systems.
b) Calculate the Cartesian unit vectors in terms of the cylindrical and spherical unit vectors.
c) Calculate the cylindrical and spherical unit vectors in terms of the Cartesian unit vectors.
Q.1 a) Calculate the scale factors for the cylindrical and spherical coordinate systems. b) Calculate the...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
1. Convert to the rectangular coordinate system a. (2,5, -5) in cylindrical b. (1,5,7) in spherical c. z= r sin 0
HINT: this problem is about using different coordinate systems to solve kinematics problems! D 4. As rod OA rotates, pin P moves along the curve BCD with a constant speed of 3 m/s (in the counterclockwise direction). The equation for this curve is r = 2/(1+cose). Solve the following for the point shown, when 0 = 1/6 (radians). 0 1m B a) Find dr/dt and do/dt, and express the velocity vector in polar coordinates. b) Find the polar unit vectors...
Practice: 1. A vector defined at (4,0,0) is expressed in Cartesian coordinate system as (2,3,0), convert it into cylindrical and spherical representations; 2. If the same vector is moved to (4,0,1), what are its cylindrical and spherical representations?
Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort...
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
cose 1. spherical coordinate system vector A= a 3 Express vectors with A right angle coordinate system
Find the divergence of the following functions in cylindrical coordinate systems: (a) r cosθ ˆ er − r sinθ ˆ eθ (b) 1/ r ˆ er
a) cartesian
b)cylindrical
c) spherical
- Y Cone, topped by sphere of radius 7 centered at origin, 90° at vertex For the region W shown in the figure above, write the limits of integration for dV in the following coordinates: JW