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19 November, 06:40

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.)

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  1. 19 November, 10:15
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    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.
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