Angular momentum conservation: determine velocity of impactor

[Vitani11]

Homework Statement

A uniform rod of length L and mass M hangs at rest from a frictionless pivot. The rod is hit a distance 0.8L below the pivot by a particle of mass m moving perpendicularly to the rod at speed v; the particle sticks to the rod. Following the collision, the maximum angle between the rod and the vertical is 90 deg. What is v?

Homework Equations

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The Attempt at a Solution

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[Vitani11]

This is where I'm at. I need another equation for t in terms of moment of inertia, mass, or radius. At least I am about 80% sure that is all I need left to solve this.

 

[Vitani11]

In case you're wondering where ω_f came from: It is the arclength equation S=rθ divided by time, where theta was given as π/2 (90 deg) and r is L.