A person lowers a bucket into a well by turning the hand crank, as the drawing illustrates. The crank handle moves with a constant tangential speed of 1.81 m/s on its circular path. The rope holding the bucket unwinds without slipping on the barrel of the crank. Find the linear speed with which the bucket moves down the well.

Assuming the handle has diameter of 0.4 m while inner part diameter is 0.1 m then the circumference of outer part is [tex]\pi d_h[/tex] where d is diameter and subscript h denote handle. By substituting 0.4 for the handle's diameter then cirxumference of outer part is [tex]\pi\times 0.4\approx 1.256 m[/tex]

The rate of rotation will then be 1.81/1.256=1.441 rev/s

Similarly, circumference of inner part will be [tex]\pi d_i[/tex] where subscript i represent inner. Substituting 0.1 for inner diameter then

[tex]\pi\times 0.1\approx 0.3142 m[/tex]

The rate of rotation found for outer handle applies for inner hence speed will be 0.3142*1.441=0.453 m/s