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  3. 3 it is important to be familiar with the use...

Question: 3 it is important to be familiar with the use...

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3. It is important to be familiar with the use of polar coordinates and be able to change between Cartesian and polar coordinates (both ways) with confidence. Lets define unit vectors along respective directions as ez, e , er and Co. Note that both types of coordinate systems here are orthogonal, so we can write the velocity vector as either one of the following forms: (a) By taking the dot product V. V using Eq. 1 and then Eq. 2, show that 2 LU (b) what are dot products ez er and Ca: ·Ca equal to? (c) Take the dot product of both Eqs. 1 and 2 with er. Equate the results, and show that we obtain (d) Repeat for dot products with e to show that (e) Equations 3 and 4 give us ur and υθ in terms of u and u. what similar tricks would you apply to obtain u and v in terms of ur and uo?

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