How many revolutions per second are needed for a centrifuge to produce an acceleration of 1 200g at a radius arm of 15.0 cm?
A)0.0280 rev/s
B)44.6 rev/s
C)14.2 rev/s
D)6.68 rev/s

Question

Quizplus · Accepted Answer

The acceleration $a$ in a centrifuge is given by the formula $a = r\omega^2$, where $r$ is the radius in meters and $\omega$ is the angular velocity in radians per second. To find $\omega$, we use $a = g \times 1200$, where $g = 9.8 \, \text{m/s}^2$. Thus, $a = 9.8 \times 1200 = 11760 \, \text{m/s}^2$. Converting $r$ to meters gives $r = 0.15 \, \text{m}$. Solving for $\omega$ gives $\omega = \sqrt{a/r} = \sqrt{11760/0.15}$. To convert $\omega$ from radians per second to revolutions per second, we divide by $2\pi$, giving $\omega/(2\pi) \approx 44.6 \, \text{rev/s}$.

How Many Revolutions Per Second Are Needed for a Centrifuge