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mae 208 test3 spring 03 solution

# mae 208 test3 spring 03 solution - SPRING 2003 MAE 208...

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SPRING 2003 ENGINEERING DYNAMICS SILVERBERG MAE 208 SOLUTION TO TEST 3 Name ______________________________ Social Security Number ________________ Instructions: Please write very neatly, show your work, and box in your answers. THEORY PROBLEM (a) ( 10 points ) Neatly draw a figure showing a general rigid body, an angular velocity vector ϖ of the rigid body, a body-fixed unit vector i 1 , the distance r between the tip of i 1 and the axis of rotation, the time derivative of i 1 denoted by d i 1 / dt , and the angle β between the angular velocity vector and the unit vector i 1 . ANSWER : dt d 1 i (b) ( 10 points ) Show that . 1 1 i ω i × = dt d ANSWER : From the figure , sin ) 1 ( , sin ) 1 ( , 1 1 1 1 β β ϖ ϖ = × = × × = = r r dt d i ω i ω i ω n i so 1 1 1 1 sin ) 1 ( sin ) 1 ( i ω i ω n i i × = × = = β ϖ ϖ β dt d dt d . i 1 ϖ r β

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(c) ( 10 points ) Show for any vector A = A 1 i 1 + A 2 i 2 + A 3 i 3 that + = bf A A ϖ x A where . 3 3 2 2 1 1 i i i A A A A bf + + = ANSWER : ( 29 ( 29 ( 29 ( 29 ( 29 . 3 3 2 2 1 1 3 3 2 2 1 1 3 3 2 2 1 1 3 3 2 2 1 1 3 3 2 2 1 1 3 3 2 2 1 1 3 3 3 3 2 2 2 2 1 1 1 1 A ω A i
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mae 208 test3 spring 03 solution - SPRING 2003 MAE 208...

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