To solve this problem we turn to the kinematic equations of angular motion.
Through them we know that the change in angular acceleration is equal to the change in velocity over a certain time, that is,
[tex]\alpha = \frac{\Delta \omega}{t}[/tex]
[tex]\alpha = \frac{\omega-\omega_0}{t}[/tex]
The information provided says that the initial angular velocity is 3890, and the final is 0 (idle)
In this way,
[tex]\alpha = \frac{0-3890/60}{10}[/tex]
It is divided by 10 because the revolutions are in minutes and the time is given in seconds.
[tex]\alpha = 6.48rev/s^2[/tex]
B) To find the number of revolutions, we know that the angular velocity is equal to the displacement in a given time, that is,
[tex]\Delta \theta = \frac{1}{2} (\omega+\omega_0)t[/tex]
[tex]\Delta \theta = \frac{1}{2} (3890/60)(10)[/tex]
[tex]\Delta \theta = 324.17rev[/tex]
The rate of deceleration is 23293 rev/min^2 while the number of revolutions is 325 rev
The angular velocity is the ratio of the angle turned to the time taken. We have the following information from the question;
ω1 = 3890rpm
ω2 = 0 rpm
t = 10 s or 0.167 mins
α = ?
Using;
ω2 = ω1 - αt
0 = 3890 - 0.167α
α = 3890/0.167 = 23293 rev/min^2
Also;
θ = [(ω1 + ω2)/2]t
θ = [(0 + 3890)/2] 0.167 mins
θ = 325 rev
Learn more about angular velocity: https://brainly.com/question/6876669
