A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.05 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.25 m/s?

Answer 1

To find the number of revolutions per second the cylinder must turn, we can use the formula for the linear speed of a point on a circle:

v = rw

Where:
v is the linear speed (0.25 m/s),
r is the radius of the cylinder (0.05 m),
w is the angular speed (in radians per second) of the cylinder.

Rearranging the equation, we have:

w = v / r

w = 0.25 m/s / 0.05 m

w = 5 rad/s

Therefore, the cylinder must turn at 5 revolutions per second.