Linear velocity in terms of angular velocity—E. By focusing on the meaning of ω ×r, both regarding its magnitude and direction, show that it equals v in Fig. 5.6. Also prove that v = ω×r can be...

Linear velocity in terms of angular velocity—E. By focusing on the meaning of ω ×r, both regarding its magnitude and direction, show that it equals v in Fig. 5.6. Also prove that v = ω×r can be expressed as the determinant in Eqn. (5.25). Angular velocity and the curl—E. Verify Eqn. (5.30), namely, that the curl of the velocity equals twice the angular velocity, which is assumed to be constant, as in rigid-body rotation. Hint: Note that the components of any position vector r in the RCCS are rx = x, ry = y, and rz = z.