Answer:
[tex]-217.508\ \text{rad/s}^2[/tex]
Explanation:
[tex]\omega_i[/tex] = Initial angular velocity = [tex]3600\times\dfrac{2\pi}{60}=377\ \text{rad/s}[/tex]
[tex]\theta[/tex] = Angular displacement = [tex]52\ \text{rev}=52\times 2\pi=326.72\ \text{rad}[/tex]
[tex]\omega_f[/tex] = Final angular velocity = 0
[tex]\alpha[/tex] = Angular acceleration
From the kinematic equations of angular motion we have
[tex]\omega_f^2-\omega_i^2=2\alpha\theta\\\Rightarrow \alpha=\dfrac{\omega_f^2-\omega_i^2}{2\theta}\\\Rightarrow \alpha=\dfrac{0-377^2}{2\times 326.72}\\\Rightarrow \alpha=-217.508\ \text{rad/s}^2[/tex]
The constant angular acceleration of the centrifuge is [tex]-217.508\ \text{rad/s}^2[/tex].
