Question

What angular speed (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm?
a. 40.7 rev's

b. 75.4 rev/s

c. 81.4 rev/s

d. 151 rev/s

Answer 1

Answer:

a. 40.7 rev's

Explanation:

"Centrifugal force" is the apparent force that a non-inertial observer seems to perceive as a result of the non-inertiality of his reference system. Therefore, in this case we must work with an equivalent force, that is, the centripetal force, which is given by:

$F_c=ma_c$

The centripetal acceleration is defined as:

$a_c=\frac{v^2}{r}$

The linear speed is given by:

$v=\omega r$

So, we have:

$a_c=\frac{(\omega r)^2}{r}\\\\a_c=\omega^2 r\\\omega=\sqrt{\frac{a_c}{r}}\\\omega=\sqrt{\frac{1000*9.8\frac{m}{s^2}}{15*10^{-2}m}}\\\omega=255.60\frac{rad}{s}\\\omega=\frac{255.60\frac{rad}{s}}{2\pi}\\\omega=40.7\frac{rev}{s}$