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

Answer:

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

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