In fact, the gravity and the centrifugal force would combine to produce a force that helps to maintain the cable exactly vertical. The counterweight, like a stone in a giant sling, would keep the cable under moderate tension to help keep it straight. An unusual material would be needed for the skyhook. A material that is both strong and light. Even the best steel is too heavy for an earth skyhook.
Crystalline graphite is presently the best candidate material for a skyhook.
Theoretically it is twenty times as strong as conventional steel and four times less dense, making it potentially 80 times better than steel for skyhook cables. Actual measurements of graphite whiskers show a tensile strength of 2.1 million newtons per square centimeter. With that strength, a one square centimeter cable of crystalline graphite could lift 210 tons in the gravity field of the earth. Partially crystalline graphite fibers imbedded in epoxy binders are presently the wonder materials of aerospace and sports equipment manufacturers. The main engines of the Space Shuttle are extremely light in weight for the amount of power they generate because they are built using graphite fibers.