Two gears are connected by a chain. The larger gear has a linear velocity of 12π/5 inches per second. The angular velocity of the smaller gear is 32π/3 radians per minute. What is the radius of the smaller gear?
The smaller gear moves through (32pi) / 3 * 1/60 = 32pi / 180 = (8/45) pi rads /sec
And the smaller gear will have the same linear velocity as the large gear
12pi / 5 = r ( 8/45) pi multiply both sides by 45/8....divide out pi
(45 * 12) / (8 * 5) = r
540 / 40 = r ≈ 13.5 in = 13.5 /12 = 1.125 ft