Question

A centrifuge in a medical laboratory rotates at an angular speed of 3,500 rev/min, clockwise (when viewed from above). When switched off, it rotates through 46.0 revolutions before coming to rest. Assuming it is constant, what is the magnitude of angular acceleration (in rad/s2)?

Answer 1

Answer:

The magnitude of angular acceleration is $232.38\ rad/s^2$.

Explanation:

Given that,

Initial angular velocity, $\omega_i=3500\ rev/min=366.5\ rad/s$

When it switched off, it comes o rest, $\omega_f=0$

Number of revolution, $\theta=46=289.02\ rad$

We need to find the magnitude of angular acceleration. It can be calculated using third equation of rotational kinematics as :

$\omega_f^2-\omega_i^2=2\alpha \theta\\\\\alpha =\dfrac{-\omega_i^2}{2\theta}\\\\\alpha =\dfrac{-(366.51)^2}{2\times 289.02}\\\\\alpha =-232.38\ rad/s^2$  

So, the magnitude of angular acceleration is $232.38\ rad/s^2$. Hence, this is the required solution.