A centrifuge 14.8 cm in diameter speed up from rest and achieves 3000 rev/min in 9.5 s. Find the distance (in m) a point on the edge of a centrifuge travels in that time.

Answered: A centrifuge 14.8 cm in diameter speed…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A centrifuge 14.8 cm in diameter speed up from rest and achieves 3000 rev/min in 9.5 s. Find the distance (in m) a point on the edge of a centrifuge travels in that time.

Expert Solution

Step 1

Given data

The diameter is $d = 14.8 cm$

The initial speed is $ω_{o} = 0 rad / s$

The final speed is $N = 3000 rev / \min$

The time is $t = 9.5 s$

The final speed is,

$\begin{array}{rcl} ω & = & \frac{2 πN}{60} \\ = & \frac{2 π (3000 rev / \min)}{60} \\ = & 314.16 rad / s \end{array}$

Step 2

The angular acceleration of motion for the centrifuge is,

$\begin{array}{rcl} α & = & \frac{ω - ω_{o}}{t} \\ = & \frac{314.16 rad / s - 0 rad / s}{9.5 s} \\ = & 33.069 rad / s^{2} \end{array}$

The angular displacement of the centrifuge is,

$\begin{array}{rcl} θ & = & ω_{o} t + \frac{1}{2} α t^{2} \\ = & (0 rad / s) (9.5 s) + \frac{1}{2} (33.069 rad / s^{2}) {(9.5 s)}^{2} \\ = & 1492.23 rad \end{array}$

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