Final answer:
The average torque necessary to bring the flywheel to rest in 20 s is approximately -0.12π N*m.
Step-by-step explanation:
To find the average torque necessary to bring the flywheel to rest, we can use the equation:
T = (I Angular acceleration) / t
Where T is the torque, I is the moment of inertia, Angular acceleration is the rate at which the angular velocity changes, and t is the time taken to bring the flywheel to rest.
First, let's find the moment of inertia using the formula:
I = 0.5 * mass * radius^2
Where mass is the mass of the flywheel and radius is the radius of the flywheel.
Substituting the given values, we have:
I = 0.5 * 5 kg * (0.2 m)^2 = 0.1 kg*m^2
Next, let's find the angular acceleration:
Angular acceleration = (final angular velocity - initial angular velocity) / t
Substituting the given values, we have:
Angular acceleration = (0 - 2π * 240rpm) / (20 s)
Angular acceleration = -24π rad/s^2
Finally, we can calculate the torque:
T = (0.1 kg*m^2 * -24π rad/s^2) / (20 s) = -0.12π N*m
Therefore, the average torque necessary to bring the flywheel to rest in 20 s is approximately -0.12π N*m.