Question

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?

Answer 1

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