Consider a industrial machine that has two gears connected by a single chain. The driving gear, that is powered by an engine, has a radius of 8.0 cm. The driven gear, that is connected to the machinery, has a radius of 16.0 cm. When the engine runs, the driving gear rotates with an angular velocity of ${\omega }_d$. Calculate the ratio of the angular velocity of the driven gear ${\omega }_f$ to the angular velocity of the driving gear ${\omega }_d$.

A sprocket has a radius of 0.2 m and an angular velocity of 10 rad/s. What is the tangential velocity at the edge?

If the linear speed of a bicycle wheel is 6 m/s and its radius is 0.3 m, what is its angular speed?

Why are the angular velocities of the pedals and middle sprocket equal?

What scenario would prevent the front wheel from spinning while the bicycle is in motion?