A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min. When switched off, it rotates through 52.0 revolutions bef

Question

A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min. When switched off, it rotates through 52.0 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge.

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Xavia 3 years 2021-09-04T12:03:17+00:00 1 Answers 14 views 0

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  1. Ladonna
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    2021-09-04T12:05:04+00:00
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    Answer:

    -217.508\ \text{rad/s}^2

    Explanation:

    \omega_i = Initial angular velocity = 3600\times\dfrac{2\pi}{60}=377\ \text{rad/s}

    \theta = Angular displacement = 52\ \text{rev}=52\times 2\pi=326.72\ \text{rad}

    \omega_f = Final angular velocity = 0

    \alpha = Angular acceleration

    From the kinematic equations of angular motion we have

    \omega_f^2-\omega_i^2=2\alpha\theta\\\Rightarrow \alpha=\dfrac{\omega_f^2-\omega_i^2}{2\theta}\\\Rightarrow \alpha=\dfrac{0-377^2}{2\times 326.72}\\\Rightarrow \alpha=-217.508\ \text{rad/s}^2

    The constant angular acceleration of the centrifuge is -217.508\ \text{rad/s}^2.

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