Angular Momentum and collisions w/o friction

[Ric]

Homework Statement

A bicycle wheel of mass M (assumed to be concentrated at its rim) and radius R is mounted horizontally so it may turn without friction on a vertical axle. A dart of mass m₀ is thrown with velocity v₀ as shown above and sticks in the tire. ( A top-view is shown to the right.)
a. What is the angular momentum of the dart about the wheel's center just before the dart strikes the rim of the wheel?
b. What is the moment of inertia of the dart and wheel system?
c. How long will it take for the wheel to make on full rotation after the collision happens?

Homework Equations

ωr=v
M R₀²

The Attempt at a Solution

Is (a) just the linear momentum of the dart multiplied by the radius?

 

[BruceW]

I don't see the picture. In what way does the dart strike the tyre?