Two gears are connected by a chain. The larger gear has a linear velocity of 27π10 inches per second. The angular velocity of the smaller gear is 15π2 radians per minute.
What is the radius of the smaller gear?
Since the gears are connected....the smaller gear will move at the same linear velocity as the larger one
So the larger gear travels 60 sec * ( 27pi /10) in /sec = 162pi in / min
So let r be the radius of the smaller gear....then
162 pi = r ( 15pi/2)
162 = r * (15/2)
r = 162 ( 2/15) = 21.6 in