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15 December, 03:24

How fast (in rpm) must a centrifuge rotate if a particle 6.00 cm from the axis of rotation is to experience an acceleration of 125,000 g's?

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  1. 15 December, 06:20
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    A particle at 6 cm from the axis of rotation has radius

    r = 6 cm = 0.06 m

    The expected acceleration is

    a = 125,000 g's = 125000 * (9.8 m/s²) = 1.225 x 10⁶ m/s²

    Let ω = the angular velocity.

    The acceleration is centripetal, and it is given by

    a = ω²r

    Therefore

    (ω rad/s) ² * (0.06 m) = 1.225 x 10⁶ m/s²

    ω² = 2.0417 x 10⁷

    ω = 4518.5 rad/s

    = (4518.5 rad/s) * (1/2π rev/rad)

    = 719.14 rev/s

    ω = (719.14 rev/s) * (60 s/min)

    = 43148.5 rpm

    Answer: 43149 rpm (nearest integer)
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