A line shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown in the diagram. If the grinder shaft must turn at 1200 rpm, what size pulley should be attached to the line shaft?
grinder shaft
the radius is r=5/2=2.5 in ------> given
Find out the circumference
C=2*pi*r
C=2*pi*2.5 ------> C=5pi in
one revolution is 5pi in
so
1200rpm is
1200*5pi=6,000pi in per minute
step 2
pulley assembly
Diameter x
250 rpm
circumference is equal to -----> C=xpi in
so
xpi*250=6,000pi
simplify
250x=6,000
x=24 in
the diameter of the pulley assembly is 24 inches