The 6-kg sphere and 4-kg block (shown in section) are secured to the arm of negligible m...

The 6-kg sphere and 4-kg 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 2-kg 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 ω₀ rad/s. Determine the angular velocity ω of the arm immediately after the plug has wedged itself in the block.