A potter's wheel with radius R_a spins at an angular speed Ω_a and touches a smaller wheel with radius R_b at its outer edges which spins at an angular speed Ω_b. What is the ratio Ω_a/Ω_b?

Consider a conveyor belt system that has two sprockets connected by a single belt. The driving sprocket which is attached to a motor has 𝑇_𝑑 of teeth and a radius of 𝑅_𝑑, and the driven sprocket which is attached to the conveyor belt, has 𝑇_𝑓 of teeth and has a radius of 𝑅_𝑓. When the motor runs, the driving sprocket rotates with an angular velocity of 𝑤_𝑑, and the driven sprocket rotates with an angular velocity of 𝑤_𝑓. Determine how the angular velocity of the driven sprocket 𝑤_𝑓 is related to the angular velocity of the driving sprocket 𝑤_𝑑 by using the value for the number of teeth located on the sprockets.

If a wheel with a radius of 0.5 m rotates at an angular velocity of 10 rad/s, what is the tangential velocity at the edge of the wheel?

A car's wheel with a radius of 0.35 m is connected to a gear system. If the gear system has a radius of 0.07 m and rotates at 1000 RPM, what is the car wheel's angular velocity?

Convert an angular velocity of 2π rad/s into RPM.