a centrifuge takes 3 minutes to accelerate uniformly from rest to its operating rational speed of 5000 rpm. How many revolutions does the ce

Question

a centrifuge takes 3 minutes to accelerate uniformly from rest to its operating rational speed of 5000 rpm. How many revolutions does the centrifuge make during this time

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Thanh Hà 3 years 2021-08-26T01:43:25+00:00 1 Answers 3 views 0

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    2021-08-26T01:44:44+00:00

    Answer:

    7500 revolutions

    Explanation:

    Given:

    Time taken for the centrifuge (t) = 3 min

    Initial angular speed of the centrifuge (ω₁) = 0 rad/min (Initially at rest)

    Final rotational speed (N₂) = 5000 rpm

    So, final angular speed of the centrifuge is given as:

    \omega_2=2\pi N_2=2\times \pi\times 5000=10000\pi\ rad/min

    Now, using the concept of angular motion, the angular acceleration is given as:

    \alpha =\dfrac{\omega_2-\omega_1}{t}\\\\\alpha =\frac{10000\pi-0}{3}\\\\\alpha=\frac{10000\pi}{3}\ rad/min^2

    Now, angular displacement of the centrifuge is determined using the angular equation of motion which is given as:

    \theta=\omega_1t+\frac{1}{2}\alpha t^2\\\\\theta=0+\frac{1}{2}\times \frac{10000\pi}{3}\times (3)^2\\\\\theta=15000\pi\ rad

    Now, we know that, 1 revolution corresponds to a angular displacement of 2π radians.

    So, 2π rad = 1 revolution

    ∴ 15000π rad = \frac{15000\pi}{2\pi}=7500\ revolutions

    Therefore, the centrifuge makes 7500 revolutions.

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