Answer to Question #260005 in Physics for Mule

Question

The sprocket wheel on the rear axle of a certain bicycle is 10 cm in diameter, and the sprocket wheel to which the pedals are attached is 20 cm in diameter. The wheels of the bicycle are 65 cm in diameter. At how many revolutions per minute must the pedals be turned to travel at 5 m/s? 

Answer 1

Determine the angular velocity of the rear wheel:

$$\omega=v/a=5/0.65=7.69\text{ rad/s}.$$

The angular velocity of the sprocket wheel with pedals must be k times lower:

$$\omega_p=\omega/k=\omega(R/r)=7.69/(20/10)=3.85\text{ rad/s},\\\space\\ n=\frac{\omega}{2\pi}·60=37\text{ rpm}.$$