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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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