Q35: Casting molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A variety of sophisticated techniques have been invented, but the basic idea is as illustrated in Figure P4.35. A cylindrical enclosure is rotated rapidly and steadily about a hori- zontal axis. Molten metal is poured into the rotating cylinder and then cooled, forming the finished prod- uct. Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bub- bles are displaced toward the axis, so unwanted voids will not be present in the casting. Sometimes it is desir- able to form a composite casting, such as for a bearing. Here a strong steel outer surface is poured and then inside it a lining of special low-friction metal. In some applications, a very strong metal is given a coating of corrosion-resistant metal. Centrifugal casting results in strong bonding between the layers.



Suppose a copper sleeve of inner radius cm and outer radius cm is to be cast. To eliminate bubbles and give high structural integrity, the cen- tripetal acceleration of each bit of metal should be at least g. What rate of rotation is required? State the answer in revolutions per minute.