A flywheel has a constant angular deceleration of 1.3 rad/^2. (b) find the angle through which the flywheel turns as it comes to rest from an angular of speed of 230 rad/s.Find the time for the flywheel to come to rest.
(a) To find the angle through which the flywheel turns as it comes to rest, we can use the equation for angular acceleration:
ω² = ω₀² + 2αθ
where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and θ is the angle through which the flywheel turns.
In this case, ω = 0 (as the flywheel comes to rest), ω₀ = 230 rad/s, and α = -1.3 rad/s² (negative because the angular acceleration is deceleration).
So, the equation becomes:
0² = (230)² + 2(-1.3)θ
0 = 52900 - 2.6θ
2.6θ = 52900
θ = 52900 / 2.6 ≈ 20346.15 rad
Therefore, the angle through which the flywheel turns as it comes to rest is approximately 20346.15 rad.
(b) To find the time for the flywheel to come to rest, we can use the equation:
ω = ω₀ + αt
where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
In this case, ω = 0 (as the flywheel comes to rest), ω₀ = 230 rad/s, and α = -1.3 rad/s².
So, the equation becomes:
0 = 230 + (-1.3)t
1.3t = 230
t = 230 / 1.3 ≈ 176.92 s
Therefore, the time for the flywheel to come to rest is approximately 176.92 seconds.