Answer:
6.55 rad/s²
Explanation:
The formula for calculating the Angular acceleration of the platform is ,
[tex]\alpha = \dfrac{\Delta \omega}{\Delta t}[/tex]
Given that, The angular speed of a rotating platform changes from w₀ = 2.8 rad/s to w = 8.8 rad/s to at a constant rate as the platform moves through an angle ∆∅ = 5.5 radians.
[tex]\Delta \omega = \omega - \omega_o[/tex]
[tex]\Delta \omega =8.8 - 2.8[/tex]
[tex]\Delta \omega =6 \: \sf \: rad/s[/tex]
Now, [tex]\Delta t[/tex] can be calculated by,
[tex]\Delta t = \dfrac{\Delta\varphi}{\Delta \omega}[/tex]
[tex]\Delta t = \dfrac{5.5}{6}[/tex]
[tex]\Delta t = 0.916 \ \sf sec [/tex]
Now we can calculate the angular acceleration of the platform:
[tex]\alpha = \dfrac{\Delta \omega}{\Delta t}[/tex]
[tex]\alpha = \dfrac{6}{0.916}[/tex]
[tex]\alpha = 6.55 \sf \ rad/s^2 [/tex]
Therefore, the angular acceleration of the platform is 6.55 rad/s²
