Urgent! Please provide me with a right answer and clear handwriting! Thanks J A

Question

Urgent! Please provide me with a right answer and clear handwriting! Thanks

J A solid cylinder of mass M and radius R has moment of inertin is rotating as shown with angular velocity wo. A small stationary ol M (just above the rotating cylinder) is dropped onto the cylinder a of mass m distance R from its center (i.e., at the rim), and sticks to it. If the comb and mass then rotate together, find the new angular velocity w.·[HINT ned cylinder : angular is conserved. Consider how the dropped mass changes the moment of inertia of the system./13 points 1o 0

Explanation / Answer

here,

mass of the cyclinder = mass of small object = M

initial angular speed is w0

let the final angular speed be w

using conservation of angular momentum

(0.5 * M * R^2) * w0 = ( 0.5 * M* R^2 + M * R^2) * w

solving for w

w = w0 /3

the new angular speed is w0 /3

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