What Is the Bullet's Velocity Before It Hits the Rotating Rod?

[jalapenojam]

A uniform thin rod of length 0.50 m and mass 4.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet's velocity makes an angle of 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 7 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact?

I think I'm supposed to use the component of the bullet's velocity that is perpendicular to the rod, but I don't know where to go from there. Any hints? Thanks!

 

[jalapenojam]

If anyone can help with any of these, I would really really appreciate it!

With center and spokes of negligible mass, a certain bicycle wheel has a thin rim of radius 0.38 m and weight 37 N. It can turn on its axle with negligible friction. A man holds the wheel above his head with the axle vertical while he stands on a turntable free to rotate without friction. The wheel rotates clockwise, as seen from above, with an angular speed of 50 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 2.1 kgm2. The man's free hand suddenly stops the rotation of the wheel (relative to the turntable). Determine the resulting angular velocity (magnitude and direction) of the system.

I don't know where to begin.