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The $14-$ lb sphere and $10-$ lb block $($shown in section$)$ are secured to the arm of negligible mass which rotates in the vertical plane about

a horizontal axis at $0.$ The $6-lb$ 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 ${}_0=2\mathrm{.}8ra\frac{d}{s}.$ Determine the angular velocity $$

$($positive if counterclockwise, negative if clockwise$)$ of the arm immediately after the plug has wedged itself in the block.

Answer: $=$

$ra\frac{d}{s}$