Question

A centrifuge in a medical laboratory rotates at an angular speed of 3,700 rev/min. When switched off, it rotates through 54.0 revolutions before coming to rest. Find the constant angular acceleration (in rad/s2) of the centrifuge. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad/s2

Answer 1

-220 rad/s²

Step-by-step explanation:

ω² = ω₀² + 2α(θ - θ₀)

We're given that ω = 0 rev/min, ω₀ = 3700 rev/min, and θ - θ₀ = 54.0 rev.

Converting to rad/s:

0 rev/min × (2π rad / rev) × (1 min / 60 s) = 0 rad/s

3700 rev/min × (2π rad / rev) × (1 min / 60 s) = 123⅓π rad/s

54.0 rev × (2π rad / rev) = 108π rad

Plugging in:

(0 rad/s)² = (123⅓π rad/s)² + 2α(108π)

α = -221.2 rad/s²

There's 2 significant figures in 3700 rev/min, so we need to round our answer to 2 sig figs. The angular acceleration is -220 rad/s².