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30 July, 06:08

There is a girl pushing on a large stone sphere. The sphere has a mass of 8200 kgand a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water. Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 30N and that the pressured water provides a frictionless support. 1) How long will it take her to rotate the sphere one time, starting from rest?

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  1. 30 July, 10:06
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    t = 35.16 s

    Explanation:

    Inertia

    I = (2/5) * m*r²

    I = (2/5) * 8200 kg * (0.9m) ²

    I = 2657 kg·m²

    τ = I*α

    30N * 0.9m = 2657kg·m² * α

    α = 0.01016 rad/s²

    Θ = ½α*t²

    2π rads = ½ * 0.01016rad/s² * t²

    t = sqrt (4π rads/0.0106rad/s²)

    t = 35.16 s
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