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Anne is working on a research project that involves the use of a centrifuge. Her samples must first experience an acceleration of 100 , but then, the acceleration must increase by a factor of six. By how much will the rotational speed have to increase? Express your answer as a fraction of the initial rotation rate.

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Hania12

Answer:

The final rotation is 2.449 times the initial rotation

Explanation:

Centripetal acceleration and rotation speed of particle is related as

a=rω²    

where ω  is angular speed and r radius of circle

Rearranging equation    

ω=[tex]\sqrt{\frac{a}{r} }[/tex]

The initial acceleration is given by

            a₁ =100g

The final acceleration of particle is

            a₂ = 6 (100g)

                  =600g

The final and initial rotation speed are related as

                  [tex]\frac{w1}{w2} =\sqrt{\frac{a2}{a1 }[/tex]

                  ω2=[tex]\sqrt{\frac{600g}{100g} } *w1[/tex]

                   ω2=2.449ω1

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