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e to ES A solid disk rotates in the horizontal plane at an angular velocity of 0

ID: 1790884 • Letter: E

Question

e to ES A solid disk rotates in the horizontal plane at an angular velocity of 0.042 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.12 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 0.43 m from the axis. The sand in the ring has a mass of 0.44 kg. After all the sand is in place, what is the angular velocity of the disk? 144 Number Units the tolerance is +/-2%

Explanation / Answer

L(angular momentum)= I ( where I =moment of inertia, =angular speed)

we will use the conservation of angular momentum to find the angular velocity of disk.

L(disk)= 0.042x0.12=5.04x 10-3 kg m^2/sec

I(sand) = MR^2= 0.44x0.43^2=0.081356 kg m^2

L ( disk and sand) = (0.12 +0.081356)

Equating the angular momentums

5.04x 10-3 =0.201356w

w =25.03 *10^-3 rad/sec