Answer:
The time it takes for the change in the angular velocity to occur is 6.5 seconds
Explanation:
From the question, we have;
The angular acceleration of the wheel, α = -4.20 rad/s²
The final angular velocity of the wheel, ω = -26.0 rad/s
From the information, we have the initial direction of rotation of the wheel = Counterclockwise
The angular displacement while the change occurs = 0 rad/s
Therefore, the initial angular velocity of the wheel, ω₀ = 0 rad/s
We have;
[tex]\alpha = \dfrac{\omega -\omega _0 }{t - t_0}[/tex]
Where;
t - t₀ = The time it takes for the change to occur
[tex]\alpha = \dfrac{\omega -0 }{t - 0}[/tex]
When t₀ = 0, we have;
t - t₀ = t
[tex]\alpha = \dfrac{\omega }{t}[/tex]
[tex]\therefore t = \dfrac{\omega}{\alpha }[/tex]
[tex]\therefore t = \dfrac{-26 \, rad/s}{-4 \, rad/s^2 } \approx 6.5 \, seconds[/tex]
The time it takes for the change in the angular velocity to occur is t - t₀ = 6.5 seconds
