Question

We could use fly wheels to store extra energy created by power plants instead of waste it- this is becoming especially important as we all become more sustainably minded. One such fly wheel has been proposed to be made of a hollow cylinder with an outer radius of 1.5 m and an inner radius of of 0.5 m. It is made of concrete with a density of 2.2X10^3 kg/m3. For it to remain stable, it is restricted to complete one rotation in 1.75s, and has negligible friction. It is designed to store 2.5MJ of rotational energy.

What is the height if this fly wheel?

Answer 1

given
R1 = 0.5 m
R2 = 1.5 m
rho = 2.2*10^3 kg/m^3
angular speed, w = 1 rotation/2.75 s

= 2*pi/2.75 rad/s

= 2.285 rad/s

let h is the height of the fly wheel.

mass of the fly wheel, m = density*volume

= rho*pi*(R2^2 - R1^2)*h

= 2.2*10^3*pi*(1.5^2 - 0.5^2)*h

= 13823*h

moment of inertia of the fly wheel, I = (1/2)*M*(R2^2 + R1^2)

= (1/2)*13823*h*(1.5^2 + 0.5^2)

= 17278.75*h

we know, energy stored in fly wheel, KE = (1/2)*I*w^2

KE = (1/2)* 17278.75*h*w^2

2.5*10^6 = (1/2)*17278.75*h*2.285^2

==> h = 55.4 m <<<<<<-------------------Answer

Note : Please comment for any further clarification.