A pulley of diameter 2.6 m rotates at 107 r/min. If it drives a follower pulley at 259 r/min, what is the diameter of the follower pulley?

To determine the diameter of the follower pulley based on the rotational speeds of the two pulleys, you can use the relationship between the diameters of the pulleys and their rotational speeds. This relationship is based on the principle of the conservation of angular momentum in a belt-driven system, where the product of the diameter and the rotational speed (in revolutions per minute, or r/min) is constant for both pulleys.

Given that the diameters and speeds of the pulley system are inversely proportional, you can set up the following formula:

(Diameter of Driver Pulley × Speed of Driver Pulley) = (Diameter of Follower Pulley × Speed of Follower Pulley).

From the information provided:

• The diameter of the driver pulley (D1) is 2.6 m and its speed (N1) is 107 r/min.

• The speed of the follower pulley (N2) is 259 r/min, and we need to find its diameter (D2).

Rearranging the formula gives us:

D2 = (D1 × N1) / N2.

Substituting the known values into this equation:

D2 = (2.6 m × 107 r/min) / 259 r