How is the angular velocity ωᵣ of the rear wheel of a bicycle related to the angular velocity ωբ of the front sprocket and pedals? Let Nբ and Nᵣ be the number of teeth on the front and rear sprockets, respectively, Fig. 10–71, and Rբ and Rᵣ their respective radii. The teeth are spaced the same on both sprockets and the rear sprocket is firmly attached to the rear wheel.

Angular velocity (ω) is a measure of how quickly an object rotates around an axis, expressed in radians per second. In the context of a bicycle, it describes the rate at which the pedals and wheels turn. The relationship between the angular velocities of different components, such as the front sprocket and rear wheel, is crucial for understanding how pedaling translates into motion.

The gear ratio is the ratio of the number of teeth on two gears that are meshed together. It determines how the angular velocities of the connected gears relate to each other. For a bicycle, the gear ratio between the front and rear sprockets affects how much the rear wheel turns for each pedal rotation, influencing speed and torque.

Mechanical advantage refers to the factor by which a mechanism multiplies the force or torque applied to it. In bicycles, the arrangement of gears provides mechanical advantage, allowing the rider to efficiently convert pedaling force into wheel rotation. Understanding this concept helps explain how different gear combinations can optimize performance for various terrains.