# 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?

Result

n =  134.4

#### Solution:

$D=1.5 \ \text{m} \ \\ v=38 \ km/h=38 / 3.6 \ m/s=10.55556 \ m/s \ \\ t=1 \ min=1 \cdot \ 60 \ s=60 \ s \ \\ \ \\ s=v \cdot \ t=10.5556 \cdot \ 60 \doteq \dfrac{ 1900 }{ 3 } \doteq 633.3333 \ \text{m} \ \\ o=\pi \cdot \ D=3.1416 \cdot \ 1.5 \doteq 4.7124 \ \text{m} \ \\ n=s/o=633.3333/4.7124 \doteq 134.3975 \doteq 134.4$

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