Question

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.

How long does it take the flywheel to reach top angular speed of 1200 rpm?

Answer 1

t = 2.95 min

Step-by-step explanation:

Given that,

The diameter of flywheeel, d = 1.5 m

Mass of flywheel, m = 250 kg

Initial angular velocity is 0

Final angular velocity,
`\omega_f=1200\ rpm = 126\ rad/s`

We need to find the time taken by the flywheel to each a speed of 1200 rpm if it starts from rest.

Firstly, we will find the angular acceleration of the flywheel.

The moment of inertia of the flywheel,

`I=(1)/(2)mr^2\\\\I=(1)/(2)* 250* (0.75)^2\\\\I=70.31\ kg-m^2`

Now,

Let the torque is 50 N-m. So,

`\alpha =(\tau)/(I)\\\\\alpha =(50)/(70.31)\\\\\alpha =0.711\ rad/s^2`

So,

`t=(\omega_f-\omega_i)/(\alpha )\\\\t=(126-0)/(0.711)\\\\t=177.21\ s`

or

t = 2.95 min