Question

Two​ pulleys, one with radius 2 inches and one with radius 7 inches​, are connected by a belt. If the 2 dash inch pulley is caused to rotate at 3 revolutions per minute​, determine the revolutions per minute of the 7 dash inch pulley. ​ (Hint: The linear speeds of the pulleys are the​ same, both equal the speed of the​ belt.)

Answer 1

6/7 revolutions per minute

Explanation:

The relative speeds are inversely proportional to the radii, so the larger pulley is rotating at 2/7 the speed of the smaller one.

larger pulley rotation rate = (3 rev/min)(2/7) = 6/7 rev/min

Answer 2

The angular speed of the 7 inch pulley is 6/7 or 0.8571 revolutions per minute.

Explanation:

Consider the provided information.

Two​ pulleys, one with radius 2 inches and one with radius 7 inches​, are connected by a belt.

It is given that r₁ = 7 in, r₂ = 2 in, ω = 3 rev/min

The angular speed of the 2 inches pulley is 3.

v₁=2×3

v₁=6

Similarly for v₂

Let the angular speed of the 7 inches pulley be ω.

Then its linear speed v₂ is:

v₂=7ω

Equate the linear speed of the pulleys as shown.

v₁=v₂

6=7ω

ω=6/7

ω=0.8571

Hence, the angular speed of the 7 inch pulley is 6/7 or 0.8571 revolutions per minute.