Physics
posted by falcon306 .
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.
Q: A motor spins up the flywheel with a constant torque of 50 {\rm N \cdot m}. How long does it take the flywheel to reach top speed? In units of seconds.

Torque = (moment of inertia) x (angular acceleration) = 50 N*m
The moment of inertia is
I = (1/2) M*R^2 = 281.25 kg*m^2
The maximum angular velocity you want to achieve is
w = 1200 rev/min * (2 pi/60) = 125.66 rad/s
The angular acceleration rate is
alpha = 125.66 rad/s / t
where t is the time required.
alpha = 50/281.25 rad/s^2 = 125.66/t
Solve for t in seconds