Math  /  Algebra

Question42. (II) How fast (in rpm) must a centrifuge rotate if a particle 8.00 cm from the axis of rotation is to experience an acceleration of 125,000 gs125,000 \mathrm{~g}^{\prime} \mathrm{s} ?

Studdy Solution
Convert ω \omega from radians per second to revolutions per minute (rpm). Use the conversion factor 1rev=2πrad 1 \, \text{rev} = 2\pi \, \text{rad} and 1min=60s 1 \, \text{min} = 60 \, \text{s} :
ωrpm=ω×602π \omega_{\text{rpm}} = \frac{\omega \times 60}{2\pi}
ωrpm=3,914.63×602π \omega_{\text{rpm}} = \frac{3,914.63 \times 60}{2\pi}
ωrpm234,877.86.2832 \omega_{\text{rpm}} \approx \frac{234,877.8}{6.2832}
ωrpm37,384.3rpm \omega_{\text{rpm}} \approx 37,384.3 \, \text{rpm}
The centrifuge must rotate at approximately:
37,384.3rpm \boxed{37,384.3 \, \text{rpm}}

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