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How fast must a centrifuge spin if a particle 8 cm from the axis of rotation...

How fast must a centrifuge spin if a particle 8 cm from the axis of rotation is to experience an acceleration of 125,000 g. (g = 9.8 m/s^2)

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Answer #1

Here, we will use the concept of centripetal acceleration as the particle is moving in a circular motion

a = mv2 / r

We know that

v = rw ( no slipping condition)

so,

a = mr2w2 / r

a = mrw2

For very small particle,

a = rw2

w = sqrt (a / r)

w = sqrt ( 125000 * 9.8 / 0.08)

w = 3913.118 rad/sec

In rpm,

w = 3913.118 * (60 / 2)

w = 37367.5

w = 37368 rpm

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