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. A motor spins up the flywheel with a constant torque of 50 N . m. How long does it take the flywheel to reach top angular speed of 1200 rpm?

SOLUTION: To solve this problem we require a some knowledge of moment of inertia and rotational kinematics and translational kinematics.The flywheel is a rigid body about central axis as shown in below figure.the initial angular speed taken as w = 0 and iinal angular speed is w = 1200 rpm.we must convert the final angular speed from rpm to rad/s then the final angular r speed will be w = (r200 rpm)(2/60) rad/s = 40 rad/s. Given data: Radius of flywheel is R = 0.75 m Mass of flywheel is M = 250 kg 2 The moment of inertia of flywheel is given by I =½ MR 2 =½ (250 kg)(0.75 m) =70.13 kg/m 2 The angular acceleration is given by = netI = (50 N/m)/(70.13 kg/m ) = 0.711 rad/s 2 The angular velocity eq using kinematics relation is given by w = w + (t t ) i r r i We can get time taken the flywheel to reach top angular speed of 1200 rpm. w i w + r(t tr) i = (40 rad/s) + 0.711 rad/s(t s 0 s ) r tr= 180 s