Anne is working on a research project that involves the use of a centrifuge. Her samples must first experience an acceleration of 100g, but then, the acceleration must increase by a factor of seven.

Question

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

Answer 1

The initial acceleration (a₁) = 100g

The final acceleration (a₂) = 7*(100g) = 700g

We know, a = rω²

So, ω = √(a/r)

Since r here is constant,

The final and initial rotation rates are related as follows-

ω_{1 /} ω₂ = √(a₁ / a₂)

So, ω_{2 = (}ω₁) / (√(a₁ / a₂))

= ₍ω₁) / (√(100g / 700g)

= 2.646 * ω₁

Therefore, the rotational speed has to increase by a factor of 2.646 times the initial rotational speed.