Animation of the particle’s movement and velocity vector (in green)

ω=0.45;
ρ=3;
r[t_]:={ρ Cos[ω t],ρ Sin[ω t]}
r[l_]:={ρ Cos[ω l/2],ρ Sin[ω l/2]}
Manipulate[
Quiet[
Show[
Graphics[{Arrow[{{0,0},r[k]}],{Green,Arrow[{r[k],r[k]+r'[k]}]}}],
 ParametricPlot[r[t],{t,0,50}],
ParametricPlot[r[l],{l,0,100}],
ListPlot[{r[k]},PlotMarkers->●,PlotStyle->Green],
PlotRange->{{-4,4},{-4,4}}
]],
{k,0,100,0.1}
]

Particle, local basis (in red), velocity vector (in green)
Remark: use the “+“ button instead of running the animation, because animation takes long to compute.

ω=0.75;
ρ=3;
r[t_]:={ρ Cos[ω t],ρ Sin[ω t]}
r[l_]:={ρ Cos[ω l/2],ρ Sin[ω l/2]}
Manipulate[
Quiet[
T[k_]:=r'[k]/(Sqrt[r'[k][[1]]^2+r'[k][[2]]^2]);
n[k_]:=T'[k]/(Sqrt[T'[k][[1]]^2+T'[k][[2]]^2]);
Show[
Graphics[{Arrow[{{0,0},r[k]}],{Green,Arrow[{r[k],r[k]+r'[k]}]},{Red,Arrow[{r[k],r[k]+T[k]}]},{Red,Arrow[{r[k],r[k]+n[k]}]}}],
 ParametricPlot[r[t],{t,0,50}],
ParametricPlot[r[l],{l,0,100}],
ListPlot[{r[k]},PlotMarkers->●,PlotStyle->Green],
PlotRange->{{-4,4},{-4,4}}
]],
{k,0,100,0.1}
]