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11 December, 11:02

A grindstone increases in angular speed from 6.00 rad/s to 12.20 rad/s in 16.00 s. Through what angle does it turn during that time if the angular acceleration is constant?

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  1. 11 December, 13:34
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    Given that the grand stone has initial angular velocity of

    w (ini) = 6rad/

    And it has a final angular velocity of

    w (fin) = 12.20rad/sec

    Time taken is t=16s

    Using equation of angular motion

    To get angular acceleration (α)

    w (fin) = w (ini) + αt

    12.20=6+16α

    16α=12.20-6

    16α=6.2

    α=6.2/16

    α=0.3875rad/sec²

    The angular acceleration is 0.39rad/s²

    Angle that he turn using

    w (fin) ²=w (ini) ²+2αθ

    12.2²=6²+2*0.3875θ

    12.2²-6²=0.775θ

    0.775θ=112.84

    Then, θ=112.84/0.775

    θ=145.6radian

    The angular displacement is 145.6rad
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