2-38. The sphere rotates in a horizontal circular path while attached to point O by a cable. When , the tangential speed of the sphere is normally distributed . Then the cable is pulled in at the constant rate of . Determine the distribution of tangential speed of the sphere in 2 seconds.

Solution: Since no force acts on the sphere along the tangent of the path, the angular momentum is conserved about point O.

Therefore, . Ans.