To find the angle through which the wheel has turned when the angular speed reaches 2.50 rad/s, we can use the concept of angular displacement. The formula for angular displacement is θ = Δω/α. Substituting the given values, the angle is approximately -0.123 radians.
To find the angle through which the wheel has turned when the angular speed reaches 2.50 rad/s, we can use the concept of angular displacement. The angular displacement is related to the initial and final angular velocities by the equation:
θ = Δω/α
Where θ is the angular displacement, Δω is the change in angular velocity, and α is the average angular acceleration. In this case, we know the initial angular velocity is 4.05 rad/s and the final angular velocity is 2.50 rad/s. We can calculate the average angular acceleration by dividing the change in angular velocity by the time it takes for the wheel to come to rest, which is given by the number of revolutions it makes:
α = (ωf - ωi) / (θ/2π)
Substituting the given values, we have:
α = (2.50 - 4.05) / (5.5 x 2π)
Once we have the average angular acceleration, we can use it to calculate the angular displacement:
θ = Δω/α = (2.50 - 4.05) / (5.5 x 2π)
Thus, the angle through which the wheel has turned when the angular speed reaches 2.50 rad/s is approximately -0.123 radians.