Question

How fast (in rpm) must a centrifuge rotate if a particle 7.6 cm from the axis of rotation is to experience an acceleration of 500000 g 's? Express your answer using two significant figures

Answer 1

DATA: (r) = (7.6 cm) (a) = [500000 g's] (g) = [9.8 m/s^1 (Because constant)] (omega) = ? (in RPM) soln \r\n we know that, for a circular motion, [acceleration (a)] = (omega^2 r) rightarrow (i) [where (r) = (radius in m) (omega) = [angular velocity in rad/sec] Here, (r) = (0.076 m) [Because (1 cm) = (10^-2 m)] (a) = (500000 g) (g) = [9.8 m/s^2] (omega) = ? Therefore (i) => (omega) = squareroot a/r = squareroot 500000 times 9.8/0.076 m/s^2 middot 1/m [8029.551 rad/sec] \r\n => (omega) = [8029.551 rad/sec] = [8029.551 (1/2 pi) rev/(1/60) min] = [8029.551 times 60/2 pi rev/min] [(77 times 10^3) rpm] Therefore (omega) = [(77 times 10^3) rpm] is speed of centrifuge upto two significant figures [Because (1 rev) = (2 pi radians) => (1 rad) = [(1/2 pi) rev] s (1 min) = (60 sec) => (1 sec) = [(1/60) min]]