A quality test has determined that a pump impeller is too heavy on one
side by an amount equal to 0.0045 kg-m. To correct this imbalance it is
recommended to cut out a groove around the outer circumference of the
impeller, using a milling machine, on the same side as the imbalance.
This will remove material with the intent of correcting the imbalance.
The dimension of the groove is 1 cm wide and 1 cm deep. The groove will
be symmetric with respect to the heavy spot. How far around the outer
circumference of the impeller should the groove be? Specify the answer
in terms of Î¸. Hint: Treat the groove as a thin ring of material.
The outer radius of the impeller, at the location of the groove, is 15 cm.
The impeller material is steel, with a density of Ï = 7900 kg/m3.