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29 May, 14:40

You push a disk-shaped platform tangentially on its edge 2.0 m from the axle. The platform starts at rest and has a rotational acceleration of 0.30 rad/s2. Determine the distance you must run while pushing the platform to increase its speed at the edge to 7.0 m/s.

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  1. 29 May, 16:32
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    Answer: 40.84 m

    Explanation:

    Given

    Radius of the disk, r = 2m

    Velocity of the disk, v = 7 rad/s

    Acceleration of the disk, α = 0.3 rad/s²

    Here, we use the formula for kinematics of rotational motion to solve

    2α (θ - θ•) = ω² - ω•²

    Where,

    ω• = 0

    ω = v/r = 7/2

    ω = 3.5 rad/s

    2 * 0.3 (θ - θ•) = 3.5² - 0

    0.6 (θ - θ•) = 12.25

    (θ - θ•) = 12.25 / 0.6

    (θ - θ•) = 20.42 rad

    Since we have both the angle and it's radius, we can calculate the arc length

    s = rθ = 2 * 20.42

    s = 40.84 m

    Thus, the needed distance is 40.84 m
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