Question

An energy storage system based on a flywheel (a rotating disk) can store a maximum of 3.9 MJ when the flywheel is rotating at 10000 revolutions per minute. What is the moment of inertia of the flywheel?

Answer 1

The maximum energy stored in the flywheel is given by the formula:

E = 1/2 * I * w^2

where E is the energy stored, I is the moment of inertia, and w is the angular velocity of the flywheel.

We are given E = 3.9 MJ and w = 10000 rev/min. First, we need to convert w to radians per second:

w = 10000 rev/min * (2*pi rad/rev) / (60 s/min) = 1047.2 rad/s

Substituting the given values into the formula, we get:

3.9 MJ = 1/2 * I * (1047.2 rad/s)^2

Solving for I, we get:

I = 3.9 MJ / (1/2 * (1047.2 rad/s)^2)

= 8.15 kg m^2

Therefore, the moment of inertia of the flywheel is 8.15 kg m^2.