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

[paulsberardi]

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.

 

[rl.bhat]

Torque T = I*α. Find the moment of inertia of the flywheel. Torque is given. Find α, and then t.

 

[kerimek]

To solve for the time it takes for the flywheel to reach its maximum speed, we can use the equation T = I*alpha, where T is torque, I is moment of inertia, and alpha is angular acceleration. We can find the moment of inertia of the flywheel using the equation I = 1/2 * m * r^2, where m is the mass and r is the radius. Plugging in the values given, we get I = 140.625 kg*m^2.

Next, we can use the equation alpha = (omega2 - omega1)/t, where omega2 is the final angular velocity, omega1 is the initial angular velocity (which is 0 in this case), and t is the time. We can rearrange this equation to solve for t, giving us t = (omega2 - omega1)/alpha. Plugging in the values, we get t = (125.7 rad/s - 0 rad/s)/(50 Nm/140.625 kg*m^2) = 2.514 seconds.

Therefore, it would take approximately 2.514 seconds for the flywheel to reach its maximum speed of 125.7 radians per second.