The angular momentum of a flywheel having a rotational inertia of 0.150 kg·m2 about its axis decreases from 3.00 to 1.400 kg·m2/s in 0.80 s.(a) What is the average torque acting on the flywheel about its central axis during this period? N·m(b) Assuming a uniform angular acceleration, through what angle will the flywheel have turned? rad(c) How much work was done on the wheel? J(d) What is the average power of the flywheel? W

(a) The average torque can be calculated using the formula for angular acceleration (α = Δω/Δt) and the relation between torque (τ) and angular acceleration (τ = Iα), where I is the moment of inertia and ω is the angular velocity.

First, we need to find the change in angular momentum (ΔL), which is the final angular momentum minus the initial angular momentum: ΔL = 1.400 kg·m2/s - 3.00 kg·m2/s = -1.60 kg·m2/s.

Then, we find the angular acceleration: α = ΔL/Δt = -1.60 kg·m2/s / 0.80 s = -2.00 rad/s².

Finally, we find the average torque: τ = Iα = 0.150 kg·m2 * -2.00 rad/s² = -0.30 N·m.

(b) The angle turned by the flywheel can be found using the formula for angular displacement (θ = ωit + 0.5α*t²), where ωi is the initial angular velocity, t is the time, and α is the angular acceleration.

First, we need to find the initial and final angular velocities. We know that L = Iω, so ω = L/I. The initial angular velocity is ωi = 3.00 kg·m2/s / 0.150 kg·m2 = 20 rad/s, and the final angular velocity is ωf = 1.400 kg·m2/s / 0.150 kg·m2 = 9.33 rad/s.

Then, we find the angle turned: θ = ωit + 0.5α*t² = 20 rad/s * 0.80 s + 0.5 * -2.00 rad/s² * (0.80 s)² = 14.4 rad.

(c) The work done on the wheel can be found using the work-energy theorem (W = ΔK), where K is the kinetic energy. The kinetic energy of a rotating object is given by K = 0.5Iω².

The initial kinetic energy is Ki = 0.5Iωi² = 0.5 * 0.150 kg·m2 * (20 rad/s)² = 30 J, and the final kinetic energy is Kf = 0.5Iωf² = 0.5 * 0.150 kg·m2 * (9.33 rad/s)² = 6.52 J.

Then, we find the work done: W = ΔK = Kf - Ki = 6.52 J - 30 J = -23.48 J.

(d) The average power can be found using the formula P = W/t, where W is the work done and t is the time.

P = W/t = -23.48 J / 0.80 s = -29.35 W.