Final answer:
To find the moment of inertia of the flywheel, use the equation T = Iα, where T is the torque, I is the moment of inertia, and α is the angular acceleration. Substitute the given values into the equations and solve for I.
Step-by-step explanation:
To find the moment of inertia of the flywheel, we can use the equation:
T = Iα
where T is the torque, I is the moment of inertia, and α is the angular acceleration.
In this case, we are given the torque and the time it takes to reach a certain angular speed, so we can calculate α using the equation:
α = ωf - ωi / t
where ωf is the final angular speed, ωi is the initial angular speed (which is 0 for a flywheel at rest), and t is the time.
Once we have α, we can substitute it into the first equation to solve for I.
Using the given values:
T = 32.0 Nm, ωf = 240.0 rpm = 240.0 * (2π rad/ min) / 60, ωi = 0, t = 12.0 s
we can calculate α and then substitute it into the equation:
I = T / α.
Your answer will be the moment of inertia of the flywheel.