IB Physics Angular momentum

A tutorial sheet of questions on angular momentum is given below.

1. Define the angular momentum of a particle about a point.
2. Define the angular momentum of a rigid body about its axis of rotation.
3. State the condition for the angular momentum of a particle about a point to be conserved.
4. Linear momentum is always parallel to the linear velocity...true or false?
5. Angular momentum is always parallel to the angular velocity...true of false.

IB Physics Rolling cylinders

A tutorial sheet of questions on rolling cylinders is given below.

1. Do ALL cylinders roll on an inclined plane with the same acceleration?
2. Does a cylinder always roll when it is released from rest on a rough inclined plane?
3. In a dynamics sense, what is the definition of rolling?
4. The coefficient of static friction between two surfaces is μ. Find the minimum angle of elevation of an inclined plane to allow a cylinder to roll down the incline.
5. Why does the coefficient of static friction appear in rolling questions?
6. A uniform pipe has a mass M and inner and outer radii a and b respectively. Find the moment of inertia of the pipe about an axis through its centre parallel to the length of the pipe.