You are designing a centrifuge to spin at a rate of 15 000 rev/min (rpm). (a) Ca

Question

You are designing a centrifuge to spin at a rate of 15 000 rev/min (rpm).

(a) Calculate the maximum centripetal acceleration that a test-tube sample held in the centrifuge arm15 cm from the rotation axis must withstand..

(b) It takes 1min and 15 s for the centrifuge to spin up to its maximum rate of revolution from rest. Calculate the magnitude of the tangential acceleration of the centrifuge while it is spinning up, assuming that the tangentialacceleration is constant.

(c) Determine the magnitude of the total acceleration at the instant when the centrifuge spins at one-half of its

maximum rotational speed and is continuing to spin up with the constant tangential acceleration found in part (b).

Explanation / Answer

W = 15000r p m = 15000 *2*3.14/60 = 1570 rad/s


a) a r= R*W^2 = 369735m/s^2


b) alpha = W/t


a_t = R*alpha = R*W/t = (0.15*1570)/75 = 3.14 m/s^2


c) W1 = W/2 = 1570/2 = 785 rad/s

a_r = R*W1^2 = 92433.75 m/s^2

a_t = 3.14m/s^2

a = sqrt(a_r^2+a_t^2) = 92433.75 rad/s^2

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