A horizontal vinyl record of mass 00878 kg and radius 0143 m

A horizontal vinyl record of mass 0.0878 kg and radius 0.143 m rotates freely about a vertical axis through its center with an angular speed of 5.03 rad/s and a rotational inertia of 4.00 x 10^-4 kg·m². Putty of mass 0.0167 kg drops vertically onto the record from above and sticks to the edge of the record.What is the angular speed of the record immediately afterwards?

Solution

Apply conservation of angular momentum to the record and puttty.

    Total initial angular momentum = Total final angular momentum

        I*W1 = (I + mr^2) W2

        (I)*W1 = (I + mr^2) W2

       W2 = (I)*W1 / (I+ mr^2)

W2 = (4*10^-4)*5.03 rad/s / (4*10^-4+ 0.0167*0.143^2 )

W2 = 2.713 rad/s