Out-of-balance forces

A disk is supported by a shaft through its geometric center O. The mass center G is not coincident with O, leading to a mass imbalance as the disk rotates. How does the mass imbalance influence the reactions on the disk at the shaft O as the shaft turns at a constant rate of Ω?

Analysis

From the above, we see that:

  • When aGy < 0 (G is above O), Fy < mg. Therefore, the vertical component of the reaction at O is less than the weight of the disk.
  • When aGy > 0 (G is below O), Fy > mg. Therefore, the vertical component of the reaction at O is greater than the weight of the disk.
  • When aGy = 0 (G is at same level as O):  Fy = mg.

Watch the animation to the right to see how Fy varies with position.