The crew of a roughly cylindrical spaceship is loading a section of the ship, with radius 2m. At times, the spaceship will spin along the cylindrical axis.

A bulkhead extends across the ship, perpendicular to the cylindrical axis. The load must be secured to the bulkhead, and there are operational constraints on the distribution of mass.

The load consists of

? a circular plate of radius 1m. It is in a fixed position, flat against the bulkhead and just touching the outer wall of the ship. It has variable density given by ?(r) = (?0)r kg/m^2 , where r is the distance to the cylindrical axis, and ?0 is a dimensionless constant.

? two small, extremely dense pieces of metal, each of which has mass 3(?0)kg. Because they are so dense, we will treat them as point masses. These may be secured in any position on the bulkhead.

We can find the moment of inertia for a flat body R of density ?, perpendicular to the z axis, rotating around the z axis using

\fThe crew of a roughly cylindrical spaceship is loading a section of the ship, with radius 2m. At times, the spaceship will spin along the cylindrical axis. A bulkhead extends across the ship, perpendicular to the cylindrical axis. The load must be secured to the bulkhead, and there are operational constraints on the distribution of mass. The load consists of . a circular plate of radius 1. It is in a fixed position, flat against the bulkhead and just touching the outer wall of the ship. It has variable density given by p(r) = porkg/m, where r is the distance to the cylindrical axis, and po is a dimensionless constant. . two small, extremely dense pieces of metal, each of which has mass 3pokg. Because they are so dense, we will treat them as point masses. These may be secured in any position on the bulkhead. We can find the moment of inertia for a flat body R of density p, perpendicular to the z axis, rotating around the z axis using 1: = (22 + 37)p(z,y) didy. a) What is the mass, centre of mass, and moment of inertia (relative to the cylindrical axis) of the plate alone? b) For this question, let po = 1. Where should the two pieces of metal be attached so that the load (plate and pieces of metal) as a whole has centre of mass located on the cylindrical axis, and moment of inertia 15kg? (Answer to the nearest centimeter.) STOP! axis of symmetry bulk head BULKHEAD IN PLAN inside ship METAL PIECES