Question

A centrifuge in a medical laboratory rotates at an angular speed of 3500 rev/min. When switched off, it rotates 46.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.

Answer 1

Answer:

The angular acceleration of the centrifuge is -231.74 rad/s².

Explanation:

Given that,

Angular speed = 3500 rev/min = 366 rad/s

We need to calculate the angular displacement

Using formula of angular displacement

$\theta=2\pi n$

Put the value into the formula

$\theta=2\pi\times46$

$\theta=289.02\ rad$

We need to calculate the angular acceleration

Using equation of motion

$\omega_{f}^2=\omega_{i}^2+2\alpha\theta$

$\alpha=\dfrac{\omega_{f}^2-\omega_{i}^2}{2\theta}$

$\alpha=\dfrac{0-(366)^2}{2\times289.02}$

$\alpha=-231.74\ rad/s^2$

Hence, The angular acceleration of the centrifuge is -231.74 rad/s².