Problem 1 Find the curl of 03x yz y xk j iv xj yi v 3The curl of v3 points in the z-directionZyXCurlTo find a possible interpretation of the curl, let us consider a body rotating with uniform angular speed w about and axis l. Let us define the vector angular velocityto be a vector of length w 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||sinq| Hence, the linear speed if P isv = w|R||sinq| = W|R||sinq|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.