Velocipedes

In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, while the rear wheel was only 45 cm. In 1891, Frederick Osmond reached a speed of 38 km/h on a bicycle, a world record. How many times a minute did the front wheel turn?

Correct result:

n =  134.4

Solution:

$$\begin{gathered} D=1.5\text{ m } \\ v=38\text{ km/h}\to \text{ m/s}=38\mathrm{/}3.6\text{ m/s}=10.55556\text{ m/s } \\ t=1\text{ min}\to \text{ s}=1\cdot 60\text{ s}=60\text{ s } \\ s=v\cdot t=10.5556\cdot 60={\displaystyle \frac{1900}{3}}\doteq 633.3333\text{ m } \\ o=\pi \cdot D=3.1416\cdot 1.5\doteq 4.7124\text{ m } \\ n=s\mathrm{/}o=633.3333\mathrm{/}4.7124=134.4 \end{gathered}$$

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