Question

(I) Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.0 min to turn through 23 complete revolutions before reaching its final speed. (a) What was its angular acceleration (assumed constant), and (b) what was its final angular speed in rpm?

Answer 1

Answer:

The angular acceleration is  $0.08rad/s^{2}$ final angular speed is $46rpm$

Explanation:

Here we know that

      $\theta= w_{o}t+\frac{1}{2}\alpha t^{2}$         .............. 1

   $\theta = 23\times 2\pi rad$

   $w_{0}=0\\t=1min =60s$

Upon substituting these values in equation  1 we get $\alpha =0.08rad/s^{2}$.

       For calculating angular velocity we know that

   $w=w_{o} + \alpha t$.

   $w=\frac{46\pi}{30}rad/s = \frac{23\pi\times60}{15\times 2 \pi} rpm = 46rpm$