Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_182

3/182 The 12-lb sphere and 8-lb block (shown in section) are secured to the arm of negligible mass which rotates in the vertical plane about a horizontal axis at O. The 4-lb plug is released from rest at A and falls into the recess in the block when the arm has reached the horizontal position. An instant before engagement, the arm has an angular velocity \(\omega_0 = 2 \text{ rad/sec}\). Determine the angular velocity \(\omega\) of the arm immediately after the plug has wedged itself in the block.