Unformatted text preview: Ã— ( r Ã— v )] = r ( v 2 + r Â· a )v ( r Â· v )r 2 a 6. Show that R (2 a r Â· Ë™r + 2 b Ë™r Â· Â¨ r ) dt = a r 2 + b Ë™r 2 + const. where r = ( x 1 , x 2 , x 3 ) and depends on t , and a and b are constants. 7. Derive the velocity and acceleration in spherical coordinates ( r, Î¸, Ï† ) where r = p x 2 + y 2 + z 2 , Î¸ = arccos z r and Ï† = arctan y x . 8. Show that âˆ‡ ( Ï†Ïˆ ) = Ï† âˆ‡ Ïˆ + Ïˆ âˆ‡ Ï† where Ïˆ and Ï† are scalars. 1...
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 Spring '07
 EdgarKnobloch
 mechanics

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