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Conservation of angular momentum gives that (Ir wr + Iw ww Irwr + Iwww = 0), which can be rearranged to say that (Iw Iw / Ir Ir = wr wr / ww ww), to find the rotational inertia the wheel should have, knowing the rocket's and wheel's maximum revolution rates, and the rocket's moment of inertia. However, the rocket's moment of inertia is relatively harder to measure, so the mass can be used to approximate.
The "ideal" moment of inertia for a given mass is (mr2) mr2. The "efficiency" of some mass as a rotational inertia can be expressed using a parameter (alpha) α, where (I = amr2αmr2), in which case (alpha) α covers the interval (0,1). We can reasonably assume that (alpha_rocket < alpha_wheel) αr < αw, as the wheel will be designed to use mass "efficiently"; rockets generally are not. Then the ratio of inertias (assuming equal radii) is given by (Ir / Iw = ar mr / aw mw). Assuming (ar < aw), (Ir / Iw < mr / mw) Ir / Iw = αrmr / αwmw. Assuming αr < αw, we have that Ir / Iw < mr / mw; that is to say, the mass ratio gives an upper bound for the rotational inertia ratio. With that in mind: The ratio in maximum revolution rates gives the ratio of masses.
Notable model inaccuracies:
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