Final answer:
The angular acceleration of the flywheel is 40.0 rad/s², calculated using α = ω / t. The torque, calculated using τ = I×α, is 2000 N·m. Note that this calculated torque does not match any of the multiple-choice options given.
Step-by-step explanation:
To find the angular acceleration (α) of the flywheel, we can use the formula α = ω / t, where ω is the final angular velocity and t is the time taken to reach this velocity.
Since the final angular velocity (ω) is 200.0 rad/s and the time (t) is 5 s, the angular acceleration is 200.0 rad/s ÷ 5 s = 40.0 rad/s².
Next, to calculate the magnitude of the torque (τ), we use the formula τ = I×α, where I is the moment of inertia of the flywheel.
Given I = 50 kg-m² and α = 40.0 rad/s², the torque is 50 kg-m² × 40.0 rad/s² = 2000 N·m.
Therefore, the correct answer is (a) 40.0 rad/s² for the angular acceleration and 2000 N·m for the torque, which is not listed among the options provided. It is possible there was a typo in the options given for torque, as none of the options correspond with the calculation based on the given data.