If the axis of rotation traverses the centre of gravity of the body, the centrifugal force exerted on that axis is nothing.
The angular velocities of the two disks and of the cross are all equal at every instant; the middle point of the cross, at A, revolves in the dotted circle described upon the line of centres C1C, as a diameter twice for each turn of the disks and cross; the instantaneous axis of rotation of the cross at any instant is at I, the point in the circle Cf C2 diametrically opposite to A.
Hence if the earths axis of rotation deviates slightly from the axis of figure, it should describe a cone about the latter in 320 sidereal days.
It is essential to the steady motion of every rapidly rotating piece in a machine that its axis of rotation should not merely traverse its centre of gravity, but should be a permanent axis; for otherwise the centrifugal couples will increass friction, produce oscillation of the shaft and tend to make it leave its bearings.
By reasoning similar to that of 30, it appears that OT is the instantaneous axis of rotation 01 the rolling cone.
These appearances he referred with great acuteness to the slight inclination of the sun's axis of rotation to the plane of the ecliptic. Thus, when the earth finds herself in the plane of the sun's equator, which occurs at two opposite points of her orbit, the spots, travelling in circles parallel with that plane, necessarily appear to describe right lines; but when the earth is above or below the equatorial level, the paths of the spots open out into curves turned downwards or upwards, according to the direction in which they are seen.
There is also a libration in latitude, arising from the fact that the axis of rotation of the moon is not precisely perpendicular to the plane of her orbit.
Centrifugal Force of a Rotating BodyThe centrifugal force exerted by a rotating body on its axis of rotation is the same in magnitude as if the mass of the body were concentrated at its centre of gravity, and acts in a plane passing through the axis of rotation and the centre of gravity of the body.