Two wheel gears are connected by a chain.

Question

Two wheel gears are connected by a chain. The larger gear has a radius of 6 centimeters and the smaller gear has a radius of 4 centimeters. The smaller gear completes 28 revolutions in 15 seconds. What is the linear velocity of each of the gears in centimeters per minute?

Answer 1

small gear: (28 rev / 15 sec) (60 sec / min) ( 2 pi radians / rev) (4 cm) = 896 pi cm/min

In other words, since there are four 15 second periods in each minute, the gear turns completely around 4 times 28 times per minute, i.e. 112 rev / min; the circumference of the circle is diameter times pi, ie. 8 pi. So the chain in contact with the small gear moves at a rate (linear velocity) of 112 x 8 pi = 896 cm/ min.

Since the chain also hews to the second, larger, gear, its linear velocity is the same!

Thought you'd have to use the 6 cm ? Only if they ask you for the rate at which the large gear is turning, e.g.. rev/sec.