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
ANSWERED
asked 2021-02-08
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?

Answers (1)

2021-02-09
\(\displaystyle\upsilon={r}\omega\)
\(\displaystyle\upsilon=\) linear speed
r=radiu
\(\displaystyle\omega=\) 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.
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