It has been suggested that we should use our power plants to generate energy in

Question

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 0.460 and outer radius 1.50 , using concrete of density 2100 . A. If, for stability, such a heavy flywheel is limited to 1.70 second for each revolution and has negligible friction at its axle, what must be its length to store 2.40 of energy in its rotational motion? B.Suppose that by strengthening the frame you could safely double the flywheel's rate of spin. What length of flywheel would you need in that case? (Solve this part without reworking the entire problem!)

Explanation / Answer

so you dont have any units anywhere so I am supposing SI for everything KE = 1/2 I w^2 I = 1/2 M (outer^2 - inner^2) = 1/2 d V (outer^2-inner^2) = 1/2 d pi L (outer^2-inner^2)^2 so 2.4 = 1/2*(1/2 *2100*pi L (1.5^2-.46^2)^2)* (2*pi/1.7)^2 solve for L L=2.56E-5 m b) if you double the spin w double so that gives a factor of 4 so L can be quarter L = 2.56E-5/4=6.4E-6

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