A flywheel has a constant angular of 1.3 rad/s^2. (a) find the angel through which the flywheel turns as it comes to rest from an angular speed of 230 rad/s. (b) 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:
θ = ω_0 * t + 0.5 * α * t^2,
where θ is the angle, ω_0 is the initial angular speed, α is the angular acceleration, and t is the time.
Given that ω_0 = 230 rad/s and α = -1.3 rad/s^2 (negative because the flywheel is slowing down), we can substitute these values into the equation:
θ = (230 rad/s) * t + 0.5 * (-1.3 rad/s^2) * t^2.
(b) To find the time for the flywheel to come to rest, we can set the final angular speed ω = 0 and solve for t in the equation:
ω = ω_0 + α * t.
Given ω = 0, ω_0 = 230 rad/s, and α = -1.3 rad/s^2, we can substitute these values into the equation:
0 = 230 rad/s + (-1.3 rad/s^2) * t.
Solving for t, we get:
-230 rad/s = (-1.3 rad/s^2) * t.
Dividing both sides by -1.3 rad/s^2, we find:
t = 230 rad/s / 1.3 rad/s^2.
Therefore, the time for the flywheel to come to rest is t = 177.7 s.