At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setting it takes t = 9.5 s to uniformly accelerate to its final angular speed ω2 = 750 rad/s.

A) Calculate the angular acceleration of the centrifuge α1 in rad/s2 over the time interval t.

B) Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the initial to the final speed.

If [tex]\omega_{1},~\omega_{2}~and~\alpha[/tex] be the initial angular speed, final angular speed and angular acceleration of the centrifuge respectively, then from rotational kinematic equation, we can write

[tex]\alpha = \dfrac{\omega_{2} - \omega_{1}}{t}......................................................(I)[/tex]

where '[tex]t[/tex]' is the time taken by the centrifuge to increase its angular speed.

Given, [tex]\omega_{i} = 250~rad~s^{-1}[/tex], [tex]\omega_{f} = 750~rad~s^{-1}[/tex] and [tex]t = 9.5~s[/tex]. From equation ([tex]I[/tex]), the angular acceleration is given by

[tex]\alpha = \dfrac{750 - 250}{9.5}~rad~s^{-2} = 5.63~rad~s^{-2}[/tex]

Part(b):

Also the angular displacement ([tex]\Delta \theta[/tex]) can be written as

[tex]&&\Delta \theta = \omega_{1}~t + \dfrac{1}{2}\alpha~t^{2}\\&or,& \Delta \theta = (250 \times 9.5 + \dfrac{1}{2} \times 5.63 \times 9.5^{2})~rad = 2629~rad[/tex]

hamzaahmeds hamzaahmeds · Answer 2 · 2021-09-27T15:54:56+02:00

This question can be solved by using the equations of motion in angular form.

A) Angular acceleration of the centrifuge is "52.63 rad/s²".

B) Angular Displacement is "4749.9 rad".

A)

To find the angular acceleration we will use the first equation of motion:

[tex]\omega_f=\omega_i+\alpha t[/tex]

where,

[tex]\alpha[/tex] = angular acceleration = ?

t = time interval = 9.5 s

[tex]\omega_f[/tex] = final angular sped = 750 rad/s

[tex]\omega_i[/tex] = initial angular speed = 250 rad/s

Therefore,

[tex]750\ rad/s = 250\ rad/s + \alpha(9.5\ s)\\\\\alpha = \frac{750\ rad/s - 250\ rad/s}{9.5\ s}[/tex]

α = 52.63 rad/s²

B)

To find angular displacement we will use the second equation of motion:

[tex]\theta = \omega_i t + \frac{1}{2}\alphat^2\\\\\theta = (250\ rad/s)(9.5\ s)+\frac{1}{2}(52.63\ rad/s^2)(9.5\ s)^2\\\\\theta = 2375\ rad + 2374.9\ rad[/tex]

θ = 4749.9 rad

Learn more about the angular motion here:

https://brainly.com/question/14979994?referrer=searchResults

The attached picture shows the angular equations of motion.