A spinning spherical shell with radius 30 cm and negligent mass is filled with 0.5kg of sand. It started spinning at an angular velocity of 8 m/s. All the sand starts within the center 10-cm and by the end has moved to the outermost radius. What is its new angular velocity?

To solve this problem, we must remember that momentum is always conserved. In this case, we use the angular momentum L:

L = m v r

Where,

L = angular momentum

m = mass

v = angular velocity

r = radius

Since L1 = L2 and m1 = m2, therefore:

v1 r2 = v2 r2

(8 m / s) (10 cm) = v2 (30 cm)

v2 = 2.67 m / s