Momentum transfer from linear to angular motion

[valovato]

I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe my physics are correct, but I am struggling with the math to figure out how to translate those 3 pieces of information into linear velocity. Please help.

 

[Gordianus]

https://en.wikipedia.org/wiki/Ballistic_pendulum