Question

# You're riding a bicycle with 13-inch radius wheels. When the speed is 44ft/sec, how many revolutions are her wheels making per one minute?

Analytic geometry
You're riding a bicycle with 13-inch radius wheels. When the speed is 44ft/sec, how many revolutions are her wheels making per one minute?

2021-02-09
$$\displaystyle\upsilon={r}\omega$$
$$\displaystyle\upsilon=$$ linear speed
$$\displaystyle\omega=$$ angular speed
Convert upsilon into inch/min:
$$\displaystyle\upsilon=\frac{{{4}{f}{t}}}{{s}}\times\frac{{{12}\in{c}{h}}}{{{1}{f}{t}}}\times\frac{{{60}{s}}}{{{1}\min}}={2880}\frac{{\in{c}{h}}}{\min}$$
Substitute into the formula
$$\displaystyle{13}\omega={2880}$$
$$\displaystyle\omega=\frac{{2880}}{{13}}\frac{{{r}{a}{d}}}{\min}$$
1revolution= $$\displaystyle{2}\pi$$ radians $$\displaystyle=\omega$$
$$\displaystyle\omega=\frac{{2880}}{{13}}\frac{{{r}{a}{d}}}{\min}\times\frac{{{1}{r}{e}{v}}}{{{2}\pi{r}{a}{d}}}$$
$$\displaystyle\approx{35.3}$$ revolutions per min.