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28 January, 22:22

a 1 m length of string is wrapped around a solid disk, of mass. 25 kg and a radius of. 30m, mounted on a frictionless axle. the string is pulled with a tension force of 20 N. what is the angular velocity of the disk after the string is pulled off

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  1. 28 January, 22:42
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    60 rad/s

    Explanation:

    ∑τ = Iα

    Fr = Iα

    For a solid disc, I = ½ mr².

    Fr = ½ mr² α

    α = 2F / (mr)

    α = 2 (20 N) / (0.25 kg * 0.30 m)

    α = 533.33 rad/s²

    The arc length is 1 m, so the angle is:

    s = rθ

    1 m = 0.30 m θ

    θ = 3.33 rad

    Use constant acceleration equation to find ω.

    ω² = ω₀² + 2αΔθ

    ω² = (0 rad/s) ² + 2 (533.33 rad/s²) (3.33 rad)

    ω = 59.6 rad/s

    Rounding to one significant figure, the angular velocity is 60 rad/s.
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