QUESTION $44\mathrm{.}1$High speed rotation is important if a flywheel is to be used as an energy storage device, given that the stored energy depends on the square of the rotational speed.$$ Appraise this statement in terms of the features that allow modern flywheels to achieve this speed. $(3)4\mathrm{.}2$ A flywheel of three uniform bars, rotating about their central points as spokes of a wheel, is made from fibres of glass with density $2200/,$ and tensile strength $3500$ MN$/$m$2.$ The fibres are aligned along the bars and held together by a minimal quantity $(10\%)$ of resin of negligible tensile strength and similar density, i$.$e$.$ the tensile strength of the bars is $90\%$ of the strength of the fibres due to the resin glue. If the generalised moment of inertia is $2$ and the moment of inertia for a uniform bar is $132,$ calculate: $($a$)$ show that the shape factor $2/3$ and hence estimate the maximum energy density obtainable. $(3)($b$)$ if the radius of the uniform bar a $=1\mathrm{.}0$ m$,$ calculate the corresponding angular velocity. $(4)$