Round your final answers to three significant figures. The operation of the Prin
ID: 1553601 • Letter: R
Question
Round your final answers to three significant figures. The operation of the Princeton Tokomak Fusion Test Reactor requires large bursts of energy The power needed exceeds the amount that can be supplied by the utility company. Prior to pulsing the reactor, energy is stored in a giant flywheel of mass7.09 x 10 kg and rotational inertia 4.19 x 10 kg m The flywheel rotates at a maximum angular speed of 358 rpm. When the stored energy is needed to operate the reactor, the flywheel is connected to an electrical generator, which converts some of the rotational kinetic energy into electric energy. (a) If the fly wheel is a uniform disk, what is its radius? (b) If the flywheel is a hollow cylinder with its mass concentrated at the rim, what is its radius?Explanation / Answer
a) for a uniform disk, I = (1/2)*M*R^2
==> R = sqrt(2*I/M)
= sqrt(2*4.19*10^6/(7.09*10^5))
= 3.44 m
b) for hollow cyllinder, I = M*R^2
==> R = sqrt(I/M)
= sqrt(4.19*10^6/(7.09*10^5))
= 2.43 m
c) w1 = 358 rpm = 358*2*pi/60 = 37.5 rad/s
w2 = 257 rpm = 257*2*pi/60 = 26.9 rad/s
average power supplied, P_avg = change in kinetic energy/time taken
= (1/2)*I*(w1^2 - w2^2)/t
= (1/2)*4.19*10^6*(37.5^2 - 26.9^2)/4.95
= 2.89*10^8 W
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