Part 6 - Generation of unbalanced centripital forces

Spin dryerA rotating body whose mass is not symmetrical about its major axis of rotation (generally the geometrical centre) will vibrate. A typical everyday example is a domestic high spin drier in which the wet load is not evenly arranged around the drum.

The vibrations that are set up can cause severe mechanical damage if allowed to continue for any period of time. Another simple example is the need to balance the wheels of a motor vehicle when tyre changes are effected to ensure a smooth ride. The equations and methods adopted to dynamically balance rotating machinery (correct placing of the ‘balancing weights’) such as flywheels, ship’s propellers, motor armatures, etc, are well documented in almost every textbook on applied mechanics 27, 36 et al.

The mathematical approach to the subject of unbalanced rotating bodies is given in Appendix 1 and Figs.10&11. The analysis clearly demonstrates that a tensile stress is set up in the rim on the heavier side and a compression stress is set up on the lighter side. Although this model does not describe tectonic movement it clearly demonstrates the differential stress pattern in the outer rim by the unbalanced rotating mass. If the induced differential stresses are large enough to exceed the hoop stress of the material of construction, catastrophic destruction of the rotating body will take place    

If the centre of the mass of the rotating earth is not coincident with it’s principal axis of rotation, then as a result of the large differential between the velocity (1675 km hr-1) at the equator and the almost negligible velocity at the polar regions, a small mass imbalance will give rise to vibration and differential stresses at the surface. The magnitude and direction of the resultant generated unbalanced forces at the surface can be calculated.

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