A centrifuge in a medical laboratory rotates at an angular speed of 5,400 rpm (revolutions per minute).When switched off,it rotates 100.0 times before coming to rest.Find the magnitude of the constant angular acceleration of the centrifuge while it slows down to a stop. A)65.0$\pi$ rad/s² B)60.0$\pi$ rad/s² C)81.0$\pi$ rad/s² D)76.0$\pi$ rad/s² E)0

Question

Quizplus · Accepted Answer

First, we need to convert the initial angular speed from rpm to rad/s:

ωi = (5400 rpm) * (2π rad/rev) / (60 s/min) = 566.37 rad/s

Then, we can use the formula for angular acceleration:

ωf^2 = ωi^2 + 2αθ

where ωf = 0 (final angular speed), θ = 100 rev (number of revolutions), and we're solving for α (angular acceleration).

Plugging in the values and solving for α, we get:

α = (ωf^2 - ωi^2) / 2θ = (0 - (566.37 rad/s)^2) / (2 * 100 rev * 2π rad/rev) ≈ 81.0 rad/s^2

Therefore, the chosen answer is C.

A Centrifuge in a Medical Laboratory Rotates at an Angular π\piπ

A Centrifuge in a Medical Laboratory Rotates at an Angular $\pi$