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## Homework Statement

It has been suggested that we should use our power plants to generate energy in the off-hours (such as late at night) and store it for use during the day. One idea put forward is to store the energy in large flywheels. Suppose we want to build such a flywheel in the shape of a hollow cylinder of inner radius 0.420m and outer radius 1.45m , using concrete of density 2150kg/m3

If, for stability, such a heavy flywheel is limited to 1.35 second for each revolution and has negligible friction at its axle, what must be its length to store 2.20MJ of energy in its rotational motion?

## Homework Equations

KE=1/2Iw^2

I=1/2(m)(R^2+R^2) the 2 different R's here

d=m/v

V=pir^2*L

## The Attempt at a Solution

So I plugged the moment of inertia formula into KE.

to get: KE=1/2(1/2*m(R^2+R^2))w^2

to get w i took 2pi/1.35

so i end up with 2.2e6=1/2(1/2)m(.42^2+1.45^2)*4.65^2

solving for m i end up with

(4*2.2e6)/(2.2789*4.65^2)=m

m=178588kg

since density is 2150 i took

2150=178588/v

solved for v and got 83m^3

took V=pi*1.45^2*L

I got 12.5 for my length, seems to be the incorrect answer

ive tried a few different things, but this method is the most logical for me

Does anyone see anything obvious wrong?