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Unformatted text preview: SPRING 2003 ENGINEERING DYNAMICS SILVERBERG MAE 208 SOLUTION TO TEST 1 THEORY PROBLEM (a) ( 10 points ) Draw a figure showing the planar path of a particle, its position vector r , the coordinates x, y, r, and , and the unit vectors i , j , n r , and n . ANSWER: (b) ( 10 points ) Show that n n = r and . r n n - = Then show that n n v v v r r + = in which . and r v r v r = = ANSWER: Differentiate with respect to time j i n sin cos + = r to get . ) cos sin ( ) (cos ) sin ( n j i j i n = +- = +- = r Similarly, differentiate with respect to time j i n cos sin +- = to get . ) sin (cos ) sin ( ) cos ( r n j i j i n - = +- =- +- = Next, differentiate the position vector r = r n r to get r r r r r r r v v r r r r n n n n n n v + = + = + = so . , r v r v r = = (c) ( 10 points ) Show that n n a...
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This note was uploaded on 08/01/2008 for the course MAE 208 taught by Professor Silverberg during the Spring '08 term at N.C. State.
- Spring '08