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9 October, 03:35

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.)

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  1. 9 October, 04:38
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    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.
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