Expert: Ahmed Salami - 1/9/2010

Question
This is a word problem for inverse and joint variation
a sprocket gear 8 in. in diameter is connected to a gear 3 in. in diameter. How fast does the smaller gear rotate when the larfer one rotates at 216 r/min? if the smaller gear is attched to a 28 in diameter rear wheel of a bicycle, how fast does the wheel rotate?(hint: r/min times circumference of gear = k)

Answer
Hi Sam,
For the gear system, the product of the rotational frequency and the circumference is always constant i.e
w . πd = k
where w is the rotational frequency and d is the diameter of the gear.
From the sprocket gear,
k = 216 . 8π
 = 1728π
For the smaller gear,
k = w . 3π
w = k/3π
 = 1728π/3π
 = 1728/3
 = 576 r/min
For the wheel,
k = w . 28π
w = k/28π
 = 1728π/28π
 = 1728/28
 = 61.7 r/min

Regards