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13 August, 20:53

A wheel initially has an angular velocity of 18 rad/s, but it is slowing at a constant rate of 2 rad/s 2. By the time it stops, it will have turned through approximately how many revolutions?

1. 65

2. 39

3. 52

4. 26

5. 13

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  1. 13 August, 20:55
    0
    5) 13 revolutions (approximately)

    Explanation:

    We apply the equations of circular motion uniformly accelerated:

    ωf² = ω₀² + 2α*θ Formula (1)

    Where:

    θ : angle that the body has rotated in a given time interval (rad)

    α : angular acceleration (rad/s²)

    ω₀ : initial angular speed (rad/s)

    ωf : final angular speed (rad/s)

    dа ta:

    ω₀ = 18 rad/s

    ωf = 0

    α = - 2 rad/s²; (-) indicates that the wheel is slowing

    Revolutions calculation that turns the wheel until it stops

    We apply the formula (1)

    ωf² = ω₀² + 2α*θ

    0 = (18) ² + 2 (-2) * θ

    4*θ = (18) ²

    θ = (18) ²/4 = 81 rad

    1 revolution = 2π rad

    θ = 81 rad * 1 revolution / 2πrad

    θ = 13 revolutions approximately
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