σ1[r_,θ_]:={r*Cos[θ],r*Sin[θ],5-r^2}
n1[r_,θ_]:=Evaluate[(0.5)*Normalize[Cross[D[σ1[r,θ],r],D[σ1[r,θ],θ]]]]
surfacePlot=ParametricPlot3D[{r*Cos[θ],r*Sin[θ],5-r^2},{r,0,2},{θ,0,2*π},Mesh->False];
normalPlot=ParametricPlot3D[n1[r,θ],{r,0,2},{θ,0,2*π},PlotStyle->Opacity[0.5]];

Show[ParametricPlot3D[{2*Cos[t],2*Sin[t],1},{t,0,2π},PlotStyle->{Thickness[0.01]},AxesOrigin->{0,0,0},Boxed->False,PlotRange->{{-2.5,2.5},{-2.5,2.5},{0,5.5}}],{surfacePlot,Graphics3D[{Arrowheads[0.025],Table[Arrow[{σ1[r,θ],σ1[r,θ]+n1[r,θ]}],{r,0.00000001,2,0.2},{θ,0,2*π,0.4}]}]}]

Show[ParametricPlot3D[{x,y,5-x},{x,-5,5},{y,-5,5},Mesh->False,PlotStyle->{Blue}],ParametricPlot3D[{3*Cos[t],3*Sin[t],z},{t,0,2π},{z,0,10},Mesh->False,PlotStyle->Opacity[0.5]],ParametricPlot3D[{3*Cos[t],3*Sin[t],5-3*Cos[t]},{t,0,2π},PlotStyle->{Red,Thickness[0.01]}]
]