Flywheel Acceleration Time Calc: Solve for Time to Reach Max Speed

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To calculate the time it takes for the flywheel to reach maximum speed, first determine the moment of inertia using the formula for a solid cylinder. Given the mass of 250 kg and a radius of 0.75 m, the moment of inertia is calculated as I = 0.5 * mass * radius^2. With a torque of 50 Nm, use the equation Torque = I * angular acceleration (α) to find α. Finally, apply the relationship between angular acceleration and time to find the time required to reach the maximum angular velocity of 125.7 radians/second.
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Homework Statement


Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. Its maximum angular velocity is 1200 rpm. A motor spins up the flywheel with a constant torque of 50 Nm. How long does it take the flywheel to reach top speed?

This gave me...
radius = .75m
mass = 250kg
max Angular Velocity = 125.7 radians/second
torque = 50 Nm

Homework Equations


I wasn't sure how to approach the problem. I was trying to figure out how to find angular acceleration, but unsure if that was possible. Please let me know the steps.
 
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Torque T = I*α. Find the moment of inertia of the flywheel. Torque is given. Find α, and then t.
 
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