Question

how fast in revolutions per minute must a centrifuge rotate in order to subject the contents of a test tube (30cm) from the axis to an acceleration equivalent to 15,000gs

Answer 1

ω=6684.51 rpm

Step-by-step explanation:

r= 30cm= 0.3m

a= 15000gs (convert to m/s^{2}

1g = 9.8 m/s^{2}

a= 15000 *9.8 = 147000 m/s^{2}

a=\frac{v^{2} }{r}

147000 = \frac{v^{2} }{0.3}

147000*0.3 = v^{2}

44100 = v^{2}

√44100 = v

210m/s = v

v=210m/s (linear velocity)

we will convert this to angular velocity

ω=\frac{v}{r}

ω= 210/0.3

ω= 700 rads^{-1}

we will convert this to rev per minute

1rad per second = 9.5493 rev per minute

ω= 700*9.5493

ω=6684.51 rpm