Question

How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000 m/s2?

Answer 1

Answer:

☆Concept:

▪︎During rotation the particle experience the outwards centrifugal force, which is due to existing centripetal force.

▪︎centipetal/centrifugal acceleration = v²/r=$\omega^{2}r$

where r is the distance from axis of rotation =7cm=$\ 7×10^{-2}$

☆solution:

• $\ a_{c}= \omega^{2}r$

• $\ 10⁵= \omega^{2}×7×10^{-2}$

• $\omega$ = $\sqrt{\dfrac{10⁷}{7}}$

• $\omega$ = $\sqrt{\dfrac{10⁶×10}{7}}$

• $\omega$ = $\ 10³ \sqrt{\dfrac{10}{7}}$

• $\omega$ = 1.2×10³rad/s

1rad/s=$\dfrac{60}{2\pi}$ rotation per min(rpm)

• $\omega$ = 1.2×10³ $\dfrac{60}{2\pi}$

》$\bf{ \omega}$ = 11.5×10³ rpm

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see the attachment also!.