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10 December, 16:16

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.)

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  1. 10 December, 16:34
    0
    The angular speed of the 7 inch pulley is 6/7 or 0.8571 revolutions per minute.

    Step-by-step 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.
  2. 10 December, 16:39
    0
    6/7 revolutions per minute

    Step-by-step 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
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