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

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:

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

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

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

So, 2π rad = 1 revolution

∴ 15000π rad =

Therefore, the centrifuge makes 7500 revolutions.

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