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Intro to Connected Wheels
12. Rotational Kinematics / Intro to Connected Wheels / Problem 2
Problem 2

Consider a conveyor belt system that has two sprockets connected by a single belt. The driving sprocket which is attached to a motor has ๐‘‡๐‘‘ of teeth and a radius of ๐‘…๐‘‘, and the driven sprocket which is attached to the conveyor belt, has ๐‘‡๐‘“ of teeth and has a radius of ๐‘…๐‘“. When the motor runs, the driving sprocket rotates with an angular velocity of ๐‘ค๐‘‘, and the driven sprocket rotates with an angular velocity of ๐‘ค๐‘“. Determine how the angular velocity of the driven sprocket ๐‘ค๐‘“ is related to the angular velocity of the driving sprocket ๐‘ค๐‘‘ by using the value for the number of teeth located on the sprockets.
Diagram of a conveyor belt system showing driving and driven sprockets with angular velocities.