A 2kg hollow sphere with a 30cm diameter is welded onto a thin 5kg rod that is 1.3m in length to form a hybrid scepter-staff for a narcissistic king. The king will often balance it in his palm with the sphere up and then let it fall over and swing down. What is the difference in linear speed of the center of mass and the outer edge of the sphere when the staff-scepter is at the bottom?
At what angle from the vertical does the weld have to accelerate the sphere faster than gravity?