Two pulleys, one with radius 2 inches and one with radius 9 inches , are connected by a belt. If the 2-inch pulley is caused to rotate at 5 revolutions per minute , determine the revolutions per minute of the 9 dash inch pulley. (Hint: The linear speeds of the pulleys are the same, both equal the speed of the belt.)

the revolutions per minute for the 9 inch pulley is 10/9.

Explanation:

Step 1:

The linear speed of the belt is

linear speed = circumference * revolutions per minute, that is

v = 2π r * ω

where

r is the radius of the pulley ω is the revolutions per minute

Therefore, the linear speed of the 2 inch pulley is:

v₂ = (2π * 2 in) * (5 rev/min)

v₂ = 4π * (5 rev/min)

Step 2:

Compute the linear speed of the belt for the 9 inch pulley:

v₈ = (2π * 9 in) * (x rev/min)

v₈ = 18π * (x rev/min)

Step 3:

Since the linear speed is the same for both pulleys, therefore

v₂ = v₈

4π * (5 rev/min) = 18π * ω₈

ω₈ = (4π * (5 rev/min)) / 18π

ω₈ = 10/9 rev/min

Therefore, the revolutions per minute for the 8 inch pulley is 10/9.