This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 3025 A Problem Set #1 Solutions 1. A circle, centered at the origin with a radius of 2 units, lies in the xy plane. Determine the unit vector in rectangular components that lies in the xy plane, is tangent to the circle at ( 3 , 1 , 0), and is in the general direction of increasing values of y : A unit vector tangent to this circle in the general increasing y direction is t = a . Its x and y components are t x = a a x = sin , and t y = a a y = cos . At the point ( 3 , 1), = 30 , and so t = sin 30 a x + cos 30 a y = 0 . 5( a x + 3 a y ) . 2. By expressing diagonals as vectors and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically oppo site corners, and passes through the center of the cube: Assuming a side length, b , two diagonal vectors would be A = b ( a x + a y + a z ) and B = b ( a x a y + a z ). Now use A B =  A  B  cos , or b 2 (1 1+1) = ( 3 b )( 3 b ) cos cos = 1 / 3 = 70 . 53 . This result (in magnitude) is the same for any two diagonal vectors. 3. A sphere of radius a , centered at the origin, rotates about the z axis at angular velocity rad/s. The rotation direction is clockwise when one is looking in the positive z direction....
View Full
Document
 Spring '08
 CITRIN

Click to edit the document details