Velocipedes

In the 19th century, bicycles had no chain drive, and the wheel axis connected the pedals directly. This wheel diameter gradually increased until the so-called high bikes (velocipedes) had a front-wheel diameter of up to 1.5 meters, while the rear wheel was only 45 cm. In 1891, Frederick Osmond reached 38 km/h on a bicycle, a world record. How many times a minute did the front wheel turn?

Correct answer:

n =  134.4

Step-by-step explanation:

$$\begin{gathered} D=1.5\text{m} \\ v=38\text{km/h}\to \text{m/s}=38:3.6\text{m/s}=10.55556\text{m/s} \\ t=1\text{min}\to \text{s}=1\cdot 60\text{s}=60\text{s} \\ s=v\cdot t=10.5556\cdot 60=\frac{1900}{3}=633\frac{1}{3}\doteq 633.3333\text{m} \\ o=\pi \cdot D=3.1416\cdot 1.5\doteq 4.7124\text{m} \\ n=s/o=633.3333/4.7124=134.4 \end{gathered}$$

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