[latex]Jeden obrot to 360^0, czyli 2pi rad\ obliczmy predkosc katowa omega\ omega=frac{Deltaalpha}{Delta t}=frac{1800*2pi}{3*60s}=20pi frac{rad}{s}\ Z kolei\ omega=frac{2pi}{T}(jeden obrot cialo wykona po czasie=okresowi)\ f=frac{1}{T}\ a)\ oxed{T=frac{2pi}{omega}\ f=frac{omega}{2pi}}\ Podstawiamy:\ oxed{T=frac{2pi}{20pifrac{rad}{s}}=0,1s}\ oxed{f=frac{1}{T}=frac{1}{0,1s}=10Hz}[/latex] [latex]b)\ v=frac{2pi r}{T}=frac{2pi romega}{2pi}=oxed{omega r}=20pifrac{rad}{s}*2m=40pifrac{m}{s}approx oxed{125,6frac{m}{s}}\ c)\ F_d=mfrac{v^2}{r}=frac{momega^2r^2}{r}=oxed{momega^2r}\ F_d=5kg*(20pifrac{rad}{s})^2*2m=4000pi^2frac{kgm}{s^2}approx oxed{39438,4N}[/latex]
[latex]dane:\m = 5 kg\n = 1800\t = 3 min = 3*60s = 180 s\r = 2 m\szukane:\a) T, f = ?\b) v = ?\c) F_{r} = ?[/latex] [latex]a)\\T = frac{t}{n} = frac{180s}{1800} = 0,1 s\\f = frac{1}{t} = frac{1}{0,1s} = 10 Hz[/latex] [latex]b)\\v = 2 pi rf\\v = 2*3,14*2m*10s^{-1}=125,6frac{m}{s}[/latex] [latex]c)\\F_{r} = frac{mv^{2}}{r}\\F_{r} = frac{5kg*(125,6frac{m}{s})^{2}}{2m}=39 438,4 Napprox39,438 kN[/latex]
