CurlTo find a possible interpretation of the curl, let us consider a body rotating with uniform angular speed e about and axis l. Let us define the vector angular velocityto be a vector of length e extending along l in the direction Take the point Oas the origin of coordinates we can write R =xi +yj +zkthe radius at which P rotates is |R||sinu| Hence, the linear speed if P isv = e|R||sinu| = O|R||sinu|If we take the curl of V, we therefore havethat isExpanding this, remembering that is a vector, we findConclusion: The angular velocity of a uniform rotating body is thus equalto one-half the curl of the linear velocity of any point of the body.( ) ( ) ( ) ( )^ ^cos sin j yz e x i yz e x ux x+ + + =w v uz y xk j iucccccc= V =^ ^ ^e( ) ( ) ( ) ( )^ ^cos sin j yz e x i yz e x ux x+ + + =( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) { }^ ^ ^^ ^ ^^ ^ ^cos cos 1 cos sinsin cos sin cos0 cos sink yz ze yz e j yz y e i yz y ek yz e xyyz e xxj yz e xzi yz e xzyz e x yz e xz y xk j iux x x xx x x xx x + + + =)`+cc +cc+ +cc+ +cc =+ +cccccc= V = eExample: For velocity field,, find the angular velocity .For the field,, we obtain: