A uniform sphere of mass m and radius R rotates around the vertical axis with angular speed w. Two particles of mass m/2 are brought close to the sphere at diametrically opposite points, at an angle theta from the vertical. The masses, which are initially essentially at rest, abruptly stick to the sphere. What angle does the resulting w make with the vertical? (If you want, you can check your answer by showing that the theta that make this angle maximum is sin^-1 (sqrt(7/9) = 61.9 degrees)