Final answer:
To stop the flywheel in 1.00 minute, a constant torque of approximately -3212.3 N⋅m (clockwise direction) would be required.
Step-by-step explanation:
The rotational kinetic energy (KE) of a spinning disk is given by the formula KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
First, we need to calculate the moment of inertia (I) for the disk, which for a uniformly thick disk is I = (1/2)mr², where m is the mass and r is the radius.
Given the mass of the disk as 82.1 kg and the radius as 1.48 m, we compute the moment of inertia using the formula. Then, considering the initial angular velocity of 297 revolutions per minute (rpm), we convert it to radians per second (ω = 2π × (297/60)).
The change in angular velocity (ω) can be obtained using the formula ω = ω₀ + αt, where ω₀ is the initial angular velocity, α is the angular acceleration, and t is time.
Since the goal is to stop the flywheel, the final angular velocity will be 0. Therefore, we rearrange the formula to solve for α. Substituting the values, we get α = -ω₀ / t.
After obtaining the angular acceleration, we use the formula τ = Iα to find the torque (τ) required to stop the flywheel. Substituting the moment of inertia and angular acceleration values, we find that a constant torque of approximately -3212.3 N⋅m (in the clockwise direction) would be necessary to stop the flywheel in 1.00 minute. The negative sign indicates that the torque would need to act in the opposite direction of the initial rotation to bring the flywheel to a stop.