Find the angular velocity of the pedal wheel of a stationary bike whose main wheel is moving at 320 ft/min. The diameter of each wheel is: main wheel 2 feet, pedal wheel 1 foot, wheel sprocket(attached to the main wheel) .5 foot.
This is not a duplicate question as this one has a picture.
This photo is not drawn to scale and not aligned.
Both the wheels i.e. Pedal as well as Main wheel will have same tangential velocities since both are attached to the same thread (or whatever you want to call it) and that thread is tangent to both the wheels.
So, Pedal wheel will have angular velocity,
$\omega=\dfrac{v}{r}=\dfrac{320\dfrac{ft}{sec}}{\dfrac{1}{2}ft}=\dfrac{640\cdot rev}{sec}$