how do you do problems in math about belts and wheels such as the following: Two wheels are connected by a belt. The smaller wheel makes 20 revolutions every 3 seconds. The belt is 30 ft long and makes one complete loop every 8 seconds. Find the diameter of the smaller wheel.

Question

amistre64 · Answer

belts are linear and wheels are angular

amistre64 · Answer

8*3 = 24

that should be a common time period to equate the 2

amistre64 · Answer

20:3   as   30:8
  *8             *3
----------------
160:24 as 90:24

amistre64 · Answer

160 revolutions = 90 feet

amistre64 · Answer

divide both sides by 160

160 revolutions = 90 feet
/160                  /160
----------------------
1 revolution = 9/16 feet

amistre64 · Answer

youve got the circumference with that, so pull off the diamer using:

C = pi d

anonymous · Answer

9/16pi ?

amistre64 · Answer

with any luck .. yes :)

anonymous · Answer

thanks so much!

amistre64 · Answer

hope its right ... it reads up right to me

ganeshie8 · Answer

i got the same answer.

small wheel : 20 revs / 3 sec => 160 revs / 24 sec
belt : 1 rev / 8 sec   => 3 rev / 24 sec (or) 3*30 ft / 24 sec

160 revs/ 24 sec = 90 ft/ 24 sec
160 revs = 90 ft
1 rev = 9/16 ft

also you may notice something interesting about BIG wheel. you can put any wheel that fits the loop. since it must be bigger than the smaller wheel, its diameter must be of range (9/16pi , 30-x)