The velocity of the point F is α1·AC, upward motion being considered positive. The velocity of the point G is −α1·CB, downward motion being negative. Hence the instantaneous axis of the sheave FG is in the diameter FG, at the distance
| FG | · | AC − BC |
| 2 | AC + BC |
from the centre towards G; the angular velocity of the sheave is
| α2 = α1 · | AC + BC | ; |
| FG |
and, consequently, the velocity of its centre is
| v2 = α2 · | FG | · | AC − BC | = | α1 (AC − BC) | , |
| 2 | AC + BC | 2 |
(42)
or the mean between the velocities of the two vertical parts of the cord.
If the cord be fixed to the framework at the point B, instead of being wound on a barrel, the velocity of W is half that of AF.
A case containing several sheaves is called a block. A fall-block is attached to a fixed point; a running-block is movable to and from a fall-block, with which it is connected by two or more plies of a rope. The whole combination constitutes a tackle or purchase. (See [Pulleys] for practical applications of these principles.)