Question

A solid disk rotates in the horizontal plane at an angular velocity of 0.036 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.17 kg · m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

Answer 1

conservation of momentum

Ii*wi=If*wf=wf(Ii+1/2 massand*.40^2)

you are given Ii, wi, masssand. Solve for wf