Speed of Rotation to Experience X Acceleration

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SUMMARY

The discussion revolves around calculating the required rotational speed of a centrifuge to achieve an acceleration of 115,000 g's for a particle located 9.00 cm from the axis of rotation. The participant converted the acceleration from g's to m/s², resulting in 11,734.7 m/s², and the radius to 0.09 m. The confusion arose from using two different equations: v=2(pi)r/T and v=sqrt(ar), leading to inconsistent results. The correct approach involves using the formula v=sqrt(ar) to find linear velocity, followed by calculating angular velocity and converting it to rpm, ultimately yielding the required speed of 3.38 x 10^4 rpm.

PREREQUISITES
  • Understanding of centripetal acceleration and its relationship to rotational motion.
  • Familiarity with the equations of motion, specifically v=2(pi)r/T and v=sqrt(ar).
  • Knowledge of unit conversions, particularly between g's and m/s².
  • Basic grasp of angular velocity and its conversion to revolutions per minute (rpm).
NEXT STEPS
  • Study the derivation and application of the centripetal acceleration formula, a= v²/r.
  • Learn how to convert linear velocity to angular velocity using the relationship v = rw.
  • Explore the process of converting angular velocity to rpm for practical applications.
  • Review examples of centrifuge calculations in physics to reinforce understanding.
USEFUL FOR

Students in physics or engineering courses, particularly those focusing on rotational dynamics and centrifuge applications, as well as educators seeking to clarify concepts related to acceleration and rotational motion.

Hisui
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Homework Statement



How fast (in rpm) must a centrifuge rotate if a particle 9.00cm from the axis of rotation is to experience an acceleration of 115,000 g's?

Homework Equations



Either v=2(pi)r/T or v=(square root)(ar) ...not knowing which of these to use is possibly my first problem...

The Attempt at a Solution



First, I converted the g's to m/s^2 and got 11,734.7m/s^2 and the radius to 0.09m... I tried solving for v with both equations above and (obviously) got two completely different answers... my notes make it look like my professor was using both, but surely for different things...?

Also, I can't seem to be able to convert this into rpm... I got the circumference to be 0.57m, so I tried to use that as one rotation, then tried using v=2(pi)r/T where T is 60s (I figured this would make it rpm)... but that gave me 0.0095m/s... which left me again with trying to figure out how to convert it into rpm... but I still don't think that's right, because the actual answer is supposed to be 3.38 x 10^4 rpm...
 
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"v=(square root)(ar)" (you can't use the other equation because you don't know T... T is not 60)

solve for v here... remember to convert r to m.

then find the angular velocity. v = rw where w is angular velocity.

then convert to rpm.
 

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