As a fist example, suppose we have a flywheel free to rotate about a horizontal axis, and that a weight m hangs by a vertical string ~1~c~g FIG.
In.; the governor is carried within the driving pulley shown at the right-hand end, while the working revolving cylinders are carried inside the boxed-in flywheel at the left-hand end, the relay cylinder and its attachments being fixed to the bed-plate in front of the flywheel.
Thus in the gyroscope the flywheel (represented by the globe in fig.
Suppose, for example, that a flywheel is rotating with angular velocity n about its axis, which is (say) horizontal, and that this axis is made to rotate with the angular velocity ~ in the horizontal plane.
The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.
If the axis of the flywheel make an angle U with the vertical, it is seen in like manner that th~ required couple in the vertical plane through the axis is Cn sin 0 ~.
Flywheels.A flywheel is a rotating piece in a machine, generally shaped like a wheel (that is to say, consisting of a rim with spokes), and suited to store and restore energy by the periodical variations in its angular velocity.
Let W be the weight of a flywheel, R its radius of gyration, ai its maximum, aj its minimum, and A=~1/8(a1+ai) its mean angular velocity.
Denote the unsteadiness of the motion of the flywheel; the denominator S of this fraction is called the steadiness.
When but one flywheel is used, it should be placed in as direct connection as possible with that part of the mechanism where the greatest amount of the periodical excess originates; but when it originates at two or more points, it is best to have a flywheel in connection with each of these points.
For example, in a machine-work, the steam-engine, which is the prime mover of the various tools, has a flywheel on the crank-shaft to store and restore the periodical excess of energy arising from the variations in the effort exerted by the connecting-rod upon the crank; and each of the slotting machines, punching machines, riveting machines, and other tools has a flywheel of its own to store and restore energy, so as to enable the very different resistances opposed to those tools at different times to be overcome without too great unsteadiness of motion.
The lever M worked from the front of the machine causes the flywheel to be connected with the driving-wheel and the machine starts.
In the case of the flywheel of a gyroscope if we neglect the friction at the bearings.