1.
[tex]Dane:\\m = 2 \ kg\\F_{d} = 30 \ N\\T = 0,1\ s\\Szukane:\\r = ?[/tex]
[tex]Rozwiazanie\\\\F_{d} = \frac{4\pi^{2} r}{T^{2}} \ \ /\cdot\frac{T^{2}}{4\pi^{2} m}\\\\r = \frac{F_{d}\cdot T^{2}}{4\pi^{2} m}\\\\r = \frac{30 \ N\cdot(0,1 \ s)^{2}}{4\cdot3,14^{2}\cdot2 \ kg}\\\\\boxed{r = 0,0038 \ m = 0,38 \ cm}[/tex]
2.
[tex]F = \frac{mv^{2}}{r}\\oraz\\F = \frac{mv_1^{2}}{3r}[/tex]
[tex]\frac{mv^{2}}{r} = \frac{mv_1^{2}}{3r} \ \ /\cdot\frac{3r}{m}\\\\v_1^{2} = 3v^{2}\\\\\boxed{v_1 = \sqrt{3v}}[/tex]
3.
[tex]Dane:\\r = 20 \ cm = 0,2 \ m\\T = 60 \ min = 60\cdot 60 \ s = 3 \ 600 \ s\\Szukane:\\v = ?\\\\v = \frac{2\pi r}{T}\\\\v = \frac{2\cdot3,14\cdot0,2 \ m}{3600 \ s}\\\\\boxed{v =0,0003 \frac{m}{s}=0,03\frac{cm}{s}}[/tex]
