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

Answer 1

7500 revolutions

Step-by-step 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* \pi* 5000=10000\pi\ rad/min`

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

`\alpha =(\omega_2-\omega_1)/(t)\\\\\alpha =(10000\pi-0)/(3)\\\\\alpha=(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+(1)/(2)\alpha t^2\\\\\theta=0+(1)/(2)* (10000\pi)/(3)* (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 =
`(15000\pi)/(2\pi)=7500\ revolutions`

Therefore, the centrifuge makes 7500 revolutions.