Speed/velocity of particles inside a centrifuge

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SUMMARY

The discussion centers on the centripetal force experienced by particles in a centrifuge, specifically analyzing four scenarios involving different particle masses and distances from the center. The consensus is that all particles maintain the same angular velocity, leading to the conclusion that the particle with the largest product of mass and radius (mr) experiences the greatest centripetal acceleration. Thus, the correct answer to the posed question is (d), contradicting the textbook's assertion that (c) is correct. The relationship between centripetal force, mass, and distance is clarified using the formula Centripetal Force = mv²/r = mrω².

PREREQUISITES
  • Understanding of centripetal force and acceleration
  • Familiarity with angular velocity and its relationship to linear speed
  • Knowledge of basic physics formulas, specifically Centripetal Force = mv²/r
  • Concept of mass distribution in rotational systems
NEXT STEPS
  • Study the derivation of the centripetal force formula in detail
  • Learn about the effects of mass and radius on centripetal acceleration
  • Explore the concept of angular momentum in rotating systems
  • Investigate real-world applications of centrifuges in laboratory settings
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, educators teaching rotational dynamics, and professionals working with centrifuge technology in scientific research.

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Which particle experiences the largest centripetal
force in a centrifuge? (3.3) K/U T/I
(a) a 0.05 g particle at a distance of 2 cm from
the centre
(b) a 0.05 g particle at a distance of 5 cm from
the centre
(c) a 0.1 g particle at a distance of 2 cm from
the centre
(d) a 0.1 g particle at a distance of 5 cm from
the centre

from our nelson gr.12 physics textbook. Book says answer is c, logically this means there is a difference in angular velocity between particles with different distance to center because centripetal acceleration= centrifugal acceleration =4pi^2*r(distance to center)*f^2(frequency)

I was wondering in a centrifuge, how are the speed/angular velocity of the particles in relation to their distance to the center of the centrifuge? Is there a formula?
 
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seems to me that in steady state all the particles should have the same angular velocity. There are no tangential forces to maintain a differential. On that basis the answer should be (d), as you have noticed. Mistakes happen.
 
Centripetal Force = mv^2/r = mrω^2 (using v=rω)

All the particles have the same angular speed, so the particle having the largest value of mr will experience the largest centripetal acceleration.

So, the answer looks like (d) and not (c).
 

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