[tex]Dane:\\m = 6 \ kg\\t = 8 \ min = 8\cdot 60 \ s = 480 \ s\\n = 120\\r = 40 \ m\\Szukane:\\a) \ T = ?\\b) \ f = ?\\c) \ \omega = ?\\d) \ v = ?\\e) \ a_{r} = ?\\f) \ F_{r} = ?\\\\Rozwiazanie[/tex]
[tex]a)\\T = \frac{t}{n}\\\\T = \frac{480 \ s}{120}\\\\\boxed{T = 4 \ s}[/tex]
[tex]b)\\f = \frac{1}{T}\\\\f = \frac{1}{4 \ s}\\\\\boxed{f = 0,25 \ Hz}\\\\lub\\\\f = \frac{n}{t} = \frac{120}{480 \ s} = 0,25 \ Hz[/tex]
[tex]c)\\\omega = \frac{2\pi}{T}\\\\\omega = \frac{2\cdot3,14}{4 \ s}\\\\\boxed{\omega = 1,57\frac{rad}{s}}[/tex]
[tex]d)\\v = \frac{2\pi r}{T}\\\\v = \frac{2\cdot3,14\cdot40 \ m}{4 \ s}\\\\\boxed{v = 62,8\frac{m}{s}}[/tex]
[tex]e)\\a_{r} = \frac{v^{2}}{r}\\\\a_{r} = \frac{(62,8\frac{m}{s})^{2}}{40 \ m}\\\\\boxed{a_{r} = 98,596\frac{m}{s^{2}}\approx98,6\frac{m}{s^{2}}}[/tex]
[tex]f)\\F_{r} = \frac{mv^{2}}{r}\\\\F_{r} = \frac{6 \ kg\cdot(62,8\frac{m}{s})^{2}}{40 \ m}\\\\\boxed{F_{r} = 591,576 \ N \approx591,6 \ N}[/tex]
