Question

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheels 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.
1. 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
2. How much energy is stored in the flywheel?

Answer 1

Answer:

176.99113 seconds

555165.24756 J

Explanation:

d = Diameter of wheel = 1.5 m

r = Radius = $\dfrac{d}{2}=\dfrac{1.5}{2}=0.75\ m$

m = Mass of wheel = 250 kg

$\tau$ = Torque = 50 Nm

$\omega$ = Angular speed = 1200 rpm

Moment of inertia is given by

$I=\dfrac{1}{2}mr^2\\\Rightarrow I=\dfrac{1}{2}250\times 0.75^2\\\Rightarrow I=70.3125\ kgm^2$

Angular acceleration is given by

$\alpha=\dfrac{\tau}{I}\\\Rightarrow \alpha=\dfrac{50}{70.3125}\\\Rightarrow \alpha=0.71\ rad/s^2$

Time taken is given by

$t=\dfrac{\omega}{\alpha}\\\Rightarrow t=\dfrac{1200\times \dfrac{2\pi}{60}}{0.71}\\\Rightarrow t=176.99113\ s$

The time it takes for the flywheel to reach top angular speed is 176.99113 seconds

Kinetic energy is given by

$K=\dfrac{1}{2}I\omega^2\\\Rightarrow K=\dfrac{1}{2}70.3125\times (1200\times \dfrac{2\pi}{60})^2\\\Rightarrow K=555165.24756\ J$

The energy is stored in the flywheel is 555165.24756 J