316 Rotation of a Rigid Object About a Fixed AxisP10.79(a)∆∆∆KKUrottrans++=0Note that initially the center of mass of the sphere is adistance hr+above the bottom of the loop; and as themass reaches the top of the loop, this distance abovethe reference level is 2Rr−.The conservation ofenergy requirement givesmg h rmg R rmvI+=++afaf2121222−ωrmhRPFIG. P10.79For the sphere Imr=252and vr=so that the expression becomesghgrgRv+7102(1)Note that hh=minwhen the speed of the sphere at the top of the loop satisfies the conditionFmgmv∑==−2afor vgRr2=−afSubstituting this into Equation (1) giveshRrRrmin+−20700.or rRmin..=270(b)When the sphere is initially at =3 and finally at point P, the conservation of energy
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