A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.0s before coming to rest. Part AIf its initial angular speed was 3890rpm, what is the magnitude of its angular deceleration? (|?| in revs/s^2) Part BHow many revolutions did the centrifuge complete after being turned off?

Question

Danika Gibbs

Physics

4 October, 00:03

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.0s before coming to rest. Part AIf its initial angular speed was 3890rpm, what is the magnitude of its angular deceleration? (|?| in revs/s^2) Part BHow many revolutions did the centrifuge complete after being turned off?

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Answers (1)

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Felicity Kirby · Answer 1

a) α = - 6.4833 rev/s²

b) n = 324 rev

Explanation:

ω₀ = 3890 rpm = (3890 rev/min) (1 min/60 s) = 64.833 rev/s

ω₁ = 0 rev/s

t = 10 s

α = ?

a) We can apply the equation:

ω₁ = ω₀ + α*t ⇒ α = (ω₁ - ω₀) / t

⇒ α = (0 rev/s - 64.833 rev/s) / 10 s

⇒ α = - 6.4833 rev/s²

b) We have to get Δθ as follows

Δθ = ω₀*t + 0.5*α*t²

⇒ Δθ = (64.833 rev/s) * (10 s) + 0.5 * ( - 6.4833 rev/s²) * (10 s) ²

⇒ Δθ = 324.1666 rev

⇒ n = 324 rev