Question

A rotating flywheel can be used as a method to store energy. If it is required that such a device be able to store up to a maximum of 2.00 x 106 J when rotating at 443 rad/s, what moment of inertia is required

Answer 1

Moment of inertia of the flywheel is equal to 10.19 kg-m^2

Step-by-step explanation:

The maximum rotational energy to be stored by the flywheel
`E_(r)` = 2.00 x 10^6 J

Angular speed with which to store this energy ω = 443 rad/s

moment of inertia of the flywheel
`I` = ?

Recall that the energy of a rotating body is gotten from the equation

`E_(r) = Iw^(2)`

Where
`E_(r)` is the rotational energy of the rotating body

`I` = moment of inertia of the body

ω = angular speed of the rotating body

imputing the values into the equation, we'll have

2.00 x 10^6 =
`I` x
`443^(2)`

2.00 x 10^6 =
`I` x 196249

`I` = (2.00 x 10^6) ÷ 196249 = 10.19 kg-m^2