A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.20 rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -26.0 rad/s. While this change occurs, the angular displacement of the wheel is zero. (Note the similarity to that of a ball being thrown vertically upward, coming to a momentary halt, and then falling downward to its initial position.) Find the time required for the change in the angular velocity to occur.

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;

Where;

t - t₀ = The time it takes for the change to occur

When t₀ = 0, we have;

t - t₀ = t

The time it takes for the change in the angular velocity to occur is t - t₀ = 6.5 seconds

need to see circuit to get time constant