fantumgrey

I'm taking a Physics test on some concepts I had to do make up work for. I have the actual answers for each question, but I still need to come up with the necessary calculations for the end result. I've tried to look through all of my notes and book, but I cannot figure out how to solve these three problems.

1) A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision? (Answer = 4.2)

2) Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot? (Answer = 12 m/s^2)

3) Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass? (Answer = 0.48 kg x m^2)

Can someone please help me out?

Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?

I know the answer is 0.48 kg x m^2, but I don't know the correct process to get it.