Question

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.

Answer 1

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=$\sqrt{\frac{a}{r} }$

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

                  $\frac{w1}{w2} =\sqrt{\frac{a2}{a1 }$

                  ω2=$\sqrt{\frac{600g}{100g} } *w1$

                   ω2=2.449ω1