Two pulleys, one with radius 3 inches and one with radius 6 inches , are connected by a belt. If the 3 dash inch pulley is caused to rotate at 4 revolutions per minute , determine the revolutions per minute of the 6 dash inch pulley. (Hint: The linear speeds of the pulleys are the same, both equal the speed of the belt.)

The angular speed of the 6 inch pulley is 2 revolutions per minute.

Step-by-step explanation:

Consider the provided information.

Two pulleys, one with radius 3 inches and one with radius 6 inches , are connected by a belt. If the 3 dash inch pulley is caused to rotate at 4 revolutions per minute ,

It is given that r₁ = 6 in, r₂ = 3 in, ω = 4 rev/min

The angular speed of the 3 inches pulley is 4.

v₁=3*4

v₁=12

Similarly for v₂

Let the angular speed of the 6 inches pulley be ω.

Then its linear speed v₂ is:

v₂=6ω

Equate the linear speed of the pulleys as shown.

v₁=v₂

12=6ω

ω=2

Hence, the angular speed of the 6 inch pulley is 2 revolutions per minute.