Respuesta :
Answer:
The time for the change in the angular velocity to occur is 14.08 secs
Explanation:
From the question,
the angular acceleration is - 4.46 rad/s²
Angular acceleration is given by the formula below
[tex]\alpha =\frac{\omega -\omega _{o} }{t - t_{o} }[/tex]
Where [tex]\alpha[/tex] is the angular acceleration
[tex]\omega[/tex] is the final angular velocity
[tex]\omega _{o}[/tex] is the initial angular velocity
[tex]t[/tex] is the final time
[tex]t_{o}[/tex] is the initial time
From the question
[tex]\alpha[/tex] = - 4.46 rad/s²
[tex]\omega _{o}[/tex] = 0 rad/s (starting from rest)
[tex]\omega[/tex] = -31.4 rad/s
[tex]t_{o}[/tex] = 0 s
Now, we will determine t
From [tex]\alpha =\frac{\omega -\omega _{o} }{t - t_{o} }[/tex], then
[tex]-4.46 = \frac{-31.4 - 0}{t - 0}[/tex]
[tex]-4.46 = \frac{-31.4}{t}[/tex]
[tex]t = \frac{-31.4}{-4.46}[/tex]
t = 7.04 secs
This is the time spent in one direction,
Since the angular displacement of the wheel is zero ( it returned to its initial position), then the time required for the change in the angular velocity will be twice this time, that is 2t
Hence,
The time is 2×7.04 secs = 14.08 secs
This is the time for the change in the angular velocity to occur.
