gears are connected by chain. The larger gear has a linear velocity of 12π/5 inches per sec. The angular velocity of the smaller gear is 32π/3 radians per min. What is the radius of the smaller gear?

Answer 1

32 Pi rad/3 min /2 Pi Rad/rev = 16/3 rev/min small gear

16/3 rev/min x min/60 sec = 4/45 rev/sec small gear

In 1 sec chain moves 12/5 Pi in

In 1 sec small gear goes 4/45 rev Diameter of small gear has to travel 12/5 Pi in as well

So 4/45 rev x Pi D = 12/5 Pi D = 27" R= 13.5 in.

I am sure that there is an easier way than shown though.