318 Rotation of a Rigid Object About a Fixed AxisP10.82Conservation of energy between apex and the point wherethe grape leaves the surface:mg ymvImgRmvmRvRffff∆=+−=+FHGIKJFHGIKJ12121121225222ωθcosafwhich gives gvRf17102FHGIKJcosaf(1)Consider the radial forces acting on the grape:mgnmvRfcos2.At the point where the grape leaves the surface, n→0.Thus, mgmvRfcos=2or vRgf2=cos.Substituting this into Equation (1) givesgggcoscosθθ710or cos=1017and =°54 0..R i∆y = R—RcosfnmgsinmgcosFIG. P10.82P10.83(a)There are not any horizontal forces acting on the rod, so the center of mass will not movehorizontally. Rather, the center of mass drops straight downward (distance h/2) with the rodrotating about the center of mass as it falls. From conservation of energy:
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .