A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad
ID: 1353064 • Letter: A
Question
A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.15 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? A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.15 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?Explanation / Answer
Apply cnservation of momentum,
final angular momentum = initial angular momentum
If*wf = Ii*wi
(0.5*0.4^2 + 0.15)*wf = 0.15*0.027
wf = 0.15*0.027/(0.5*0.4^2 + 0.15)
= 0.0176 rad/s <<<<<-------Answer
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