How fast (in rpm) must a centrifuge rotate if a particle 6.66cm from the axis of

Question

How fast (in rpm) must a centrifuge rotate if a particle 6.66cm from the axis of rotation is to experience an acceleration of104000g's? Ok for this question I multiplied the acceleration by9.81m/s^2 to get it in terms of g. Then I used the equation forcentripetal accelertion. a=v^2/r. I then multiplied .0666 m by theacceleration I calculated and took the sqrt.To convert from m/s torpm I divided by 2pi(rad)m and multipled by 60 sec. Where did I gowrong? How fast (in rpm) must a centrifuge rotate if a particle 6.66cm from the axis of rotation is to experience an acceleration of104000g's? Ok for this question I multiplied the acceleration by9.81m/s^2 to get it in terms of g. Then I used the equation forcentripetal accelertion. a=v^2/r. I then multiplied .0666 m by theacceleration I calculated and took the sqrt.To convert from m/s torpm I divided by 2pi(rad)m and multipled by 60 sec. Where did I gowrong?

Explanation / Answer

So...I'll just do it, you can follow my math: 104000 * 9.8 = 1019200 a = v^2 / r v^2 = a*r v = sqrt(a*r) v = sqrt(1019200 * .0666) v = 260.5 m/s Then divide that by the circumference to get cycles per second: 260.5 / (2r) = 260.5 / (2*.0666)    = 622 cycles per second 622 cycles per second * 60 seconds per minute = 37356 rpm or 37400rpm for sig figs. PM me if that's not right.

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